diff options
| author | Enrico Tassi | 2019-05-22 13:43:08 +0200 |
|---|---|---|
| committer | Enrico Tassi | 2019-05-22 15:34:14 +0200 |
| commit | 748d716efb2f2f75946c8386e441ce1789806a39 (patch) | |
| tree | fe7bb1c5235550410c64e968f4a4d69b7f10a047 /docs/htmldoc/mathcomp.fingroup.action.html | |
| parent | 415be3b908daadabf178a292c885db78e5b2c9a4 (diff) | |
htmldoc regenerated
Diffstat (limited to 'docs/htmldoc/mathcomp.fingroup.action.html')
| -rw-r--r-- | docs/htmldoc/mathcomp.fingroup.action.html | 1100 |
1 files changed, 546 insertions, 554 deletions
diff --git a/docs/htmldoc/mathcomp.fingroup.action.html b/docs/htmldoc/mathcomp.fingroup.action.html index 4531510..578c356 100644 --- a/docs/htmldoc/mathcomp.fingroup.action.html +++ b/docs/htmldoc/mathcomp.fingroup.action.html @@ -21,7 +21,6 @@ <div class="code"> <span class="comment">(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. <br/> Distributed under the terms of CeCILL-B. *)</span><br/> -<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="mathcomp.ssreflect.ssreflect.html#"><span class="id" title="library">mathcomp.ssreflect.ssreflect</span></a>.<br/> <br/> </div> @@ -151,23 +150,23 @@ <span class="id" title="keyword">Section</span> <a name="ActionDef"><span class="id" title="section">ActionDef</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="ActionDef.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActionDef.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="ActionDef.rT"><span class="id" title="variable">rT</span></a> : <span class="id" title="keyword">Type</span>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="ActionDef.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActionDef.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="ActionDef.rT"><span class="id" title="variable">rT</span></a> : <span class="id" title="keyword">Type</span>).<br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.aT"><span class="id" title="variable">aT</span></a>.<br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.rT"><span class="id" title="variable">rT</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="act_morph"><span class="id" title="definition">act_morph</span></a> <span class="id" title="var">to</span> <span class="id" title="var">x</span> := <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span>, <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="act_morph"><span class="id" title="definition">act_morph</span></a> <span class="id" title="var">to</span> <span class="id" title="var">x</span> := <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span>, <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="is_action"><span class="id" title="definition">is_action</span></a> <span class="id" title="var">to</span> :=<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#left_injective"><span class="id" title="definition">left_injective</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#act_morph"><span class="id" title="definition">act_morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_injective"><span class="id" title="definition">left_injective</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#act_morph"><span class="id" title="definition">act_morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Record</span> <a name="action"><span class="id" title="record">action</span></a> := <a name="Action"><span class="id" title="constructor">Action</span></a> {<a name="act"><span class="id" title="projection">act</span></a> :> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.rT"><span class="id" title="variable">rT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.rT"><span class="id" title="variable">rT</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="method">act</span></a>}.<br/> +<span class="id" title="keyword">Record</span> <a name="action"><span class="id" title="record">action</span></a> := <a name="Action"><span class="id" title="constructor">Action</span></a> {<a name="act"><span class="id" title="projection">act</span></a> :> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.rT"><span class="id" title="variable">rT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDef.rT"><span class="id" title="variable">rT</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="method">act</span></a>}.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="clone_action"><span class="id" title="definition">clone_action</span></a> <span class="id" title="var">to</span> :=<br/> - <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <span class="id" title="var">_</span> <span class="id" title="var">toP</span> := <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">type</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">for</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <span class="id" title="tactic">in</span><br/> + <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <span class="id" title="var">_</span> <span class="id" title="var">toP</span> := <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">type</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">for</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <span class="id" title="tactic">in</span><br/> <span class="id" title="keyword">fun</span> <span class="id" title="var">k</span> ⇒ <a class="idref" href="mathcomp.fingroup.action.html#k"><span class="id" title="variable">k</span></a> <span class="id" title="var">toP</span>.<br/> <br/> @@ -183,11 +182,11 @@ <span class="id" title="keyword">Delimit</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">action_scope</span> <span class="id" title="keyword">with</span> <span class="id" title="var">act</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">"</span></a>{ 'action' aT &-> T }" := (<a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#26c09fa7b21f5311d68f07b2527cd1eb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#26c09fa7b21f5311d68f07b2527cd1eb"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#26c09fa7b21f5311d68f07b2527cd1eb"><span class="id" title="notation">:</span></a> <span class="id" title="var">aT</span><a class="idref" href="mathcomp.ssreflect.finset.html#26c09fa7b21f5311d68f07b2527cd1eb"><span class="id" title="notation">]</span></a> <span class="id" title="var">T</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="5567a34191268487a9ef0120f668a04c"><span class="id" title="notation">"</span></a>{ 'action' aT &-> T }" := (<a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <span class="id" title="var">aT</span><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">]</span></a> <span class="id" title="var">T</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "{ 'action' aT &-> T }") : <span class="id" title="var">type_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">"</span></a>[ 'action' 'of' to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#clone_action"><span class="id" title="definition">clone_action</span></a> (@<a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">to</span>))<br/> +<span class="id" title="keyword">Notation</span> <a name="ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">"</span></a>[ 'action' 'of' to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#clone_action"><span class="id" title="definition">clone_action</span></a> (@<a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">to</span>))<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'action' 'of' to ]") : <span class="id" title="var">form_scope</span>.<br/> <br/> @@ -197,8 +196,8 @@ <span class="id" title="keyword">Section</span> <a name="TotalAction"><span class="id" title="section">TotalAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="TotalAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="TotalAction.rT"><span class="id" title="variable">rT</span></a> : <span class="id" title="keyword">Type</span>) (<a name="TotalAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>).<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="TotalAction.to1"><span class="id" title="variable">to1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#TotalAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>) (<a name="TotalAction.toM"><span class="id" title="variable">toM</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#act_morph"><span class="id" title="definition">act_morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="TotalAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="TotalAction.rT"><span class="id" title="variable">rT</span></a> : <span class="id" title="keyword">Type</span>) (<a name="TotalAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>).<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="TotalAction.to1"><span class="id" title="variable">to1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#TotalAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>) (<a name="TotalAction.toM"><span class="id" title="variable">toM</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#act_morph"><span class="id" title="definition">act_morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="is_total_action"><span class="id" title="lemma">is_total_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalAction.to"><span class="id" title="variable">to</span></a>.<br/> @@ -213,47 +212,47 @@ <span class="id" title="keyword">Section</span> <a name="ActionDefs"><span class="id" title="section">ActionDefs</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="ActionDefs.aT"><span class="id" title="variable">aT</span></a> <a name="ActionDefs.aT'"><span class="id" title="variable">aT'</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActionDefs.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="ActionDefs.D'"><span class="id" title="variable">D'</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT'"><span class="id" title="variable">aT'</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="ActionDefs.aT"><span class="id" title="variable">aT</span></a> <a name="ActionDefs.aT'"><span class="id" title="variable">aT'</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActionDefs.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="ActionDefs.D'"><span class="id" title="variable">D'</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT'"><span class="id" title="variable">aT'</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="morph_act"><span class="id" title="definition">morph_act</span></a> <span class="id" title="var">rT</span> <span class="id" title="var">rT'</span> (<span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">to'</span> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D'"><span class="id" title="variable">D'</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT'"><span class="id" title="variable">rT'</span></a>) <span class="id" title="var">f</span> <span class="id" title="var">fA</span> :=<br/> - <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to'"><span class="id" title="variable">to'</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#fA"><span class="id" title="variable">fA</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> + <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to'"><span class="id" title="variable">to'</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#fA"><span class="id" title="variable">fA</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> <span class="id" title="keyword">Variable</span> <a name="ActionDefs.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>. <span class="comment">(* Most definitions require a finType structure on rT *)</span><br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.rT"><span class="id" title="variable">rT</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="actm"><span class="id" title="definition">actm</span></a> <span class="id" title="var">to</span> <span class="id" title="var">a</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="actm"><span class="id" title="definition">actm</span></a> <span class="id" title="var">to</span> <span class="id" title="var">a</span> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="setact"><span class="id" title="definition">setact</span></a> <span class="id" title="var">to</span> <span class="id" title="var">S</span> <span class="id" title="var">a</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="setact"><span class="id" title="definition">setact</span></a> <span class="id" title="var">to</span> <span class="id" title="var">S</span> <span class="id" title="var">a</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="orbit"><span class="id" title="definition">orbit</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> <span class="id" title="var">x</span> := <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="orbit"><span class="id" title="definition">orbit</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> <span class="id" title="var">x</span> := <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="amove"><span class="id" title="definition">amove</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="amove"><span class="id" title="definition">amove</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="afix"><span class="id" title="definition">afix</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="afix"><span class="id" title="definition">afix</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]]</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="astab"><span class="id" title="definition">astab</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="astab"><span class="id" title="definition">astab</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]]</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="astabs"><span class="id" title="definition">astabs</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#aa0c936d7feb8f26825e601735c0125f"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="astabs"><span class="id" title="definition">astabs</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="acts_on"><span class="id" title="definition">acts_on</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="acts_on"><span class="id" title="definition">acts_on</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="atrans"><span class="id" title="definition">atrans</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="atrans"><span class="id" title="definition">atrans</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="faithful"><span class="id" title="definition">faithful</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#astab"><span class="id" title="definition">astab</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#c33afa16525556de4ed568ad52c9389f"><span class="id" title="notation">[1]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="faithful"><span class="id" title="definition">faithful</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#astab"><span class="id" title="definition">astab</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#b54f5e35cb228bba5934c852e0951c39"><span class="id" title="notation">[1]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#ActionDefs"><span class="id" title="section">ActionDefs</span></a>.<br/> @@ -261,12 +260,12 @@ <br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">"</span></a>to ^*" := (<a class="idref" href="mathcomp.fingroup.action.html#setact"><span class="id" title="definition">setact</span></a> <span class="id" title="var">to</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "to ^*") : <span class="id" title="var">fun_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">"</span></a>to ^*" := (<a class="idref" href="mathcomp.fingroup.action.html#setact"><span class="id" title="definition">setact</span></a> <span class="id" title="var">to</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "to ^*") : <span class="id" title="var">fun_scope</span>.<br/> <br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">"</span></a>''Fix_' to ( A )" := (<a class="idref" href="mathcomp.fingroup.action.html#afix"><span class="id" title="definition">afix</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">"</span></a>''Fix_' to ( A )" := (<a class="idref" href="mathcomp.fingroup.action.html#afix"><span class="id" title="definition">afix</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">to</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "''Fix_' to ( A )") : <span class="id" title="var">group_scope</span>.<br/> <br/> @@ -276,63 +275,63 @@ camlp4 grammar factoring </div> <div class="code"> -<span class="id" title="keyword">Notation</span> <a name="ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">"</span></a>''Fix_' ( to ) ( A )" := <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a><br/> +<span class="id" title="keyword">Notation</span> <a name="6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">"</span></a>''Fix_' ( to ) ( A )" := <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a><br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">"</span></a>''Fix_' ( S | to ) ( A )" := (<span class="id" title="var">S</span> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">"</span></a>''Fix_' ( S | to ) ( A )" := (<span class="id" title="var">S</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''Fix_' ( S | to ) ( A )") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">"</span></a>''Fix_' to [ a ]" := (<a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">"</span></a>''Fix_' to [ a ]" := (<a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">to</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "''Fix_' to [ a ]") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">"</span></a>''Fix_' ( S | to ) [ a ]" := (<span class="id" title="var">S</span> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">"</span></a>''Fix_' ( S | to ) [ a ]" := (<span class="id" title="var">S</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">]</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''Fix_' ( S | to ) [ a ]") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">"</span></a>''C' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astab"><span class="id" title="definition">astab</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">"</span></a>''C' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astab"><span class="id" title="definition">astab</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''C' ( S | to )") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="652d6cc67746e5361142d90686607781"><span class="id" title="notation">"</span></a>''C_' A ( S | to )" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">"</span></a>''C_' A ( S | to )" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "''C_' A ( S | to )") : <span class="id" title="var">group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="44caf6cd334a2a1e387cb945c4fdb874"><span class="id" title="notation">"</span></a>''C_' ( A ) ( S | to )" := <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a><br/> +<span class="id" title="keyword">Notation</span> <a name="5ac5649c0c6722396ef7b09fb95efc38"><span class="id" title="notation">"</span></a>''C_' ( A ) ( S | to )" := <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a><br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">"</span></a>''C' [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">"</span></a>''C' [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''C' [ x | to ]") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">"</span></a>''C_' A [ x | to ]" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">"</span></a>''C_' A [ x | to ]" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "''C_' A [ x | to ]") : <span class="id" title="var">group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="1fb3703b929cf964cd25eac50eea7151"><span class="id" title="notation">"</span></a>''C_' ( A ) [ x | to ]" := <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a><br/> +<span class="id" title="keyword">Notation</span> <a name="24b4379335336f15427bd11e0177a7fb"><span class="id" title="notation">"</span></a>''C_' ( A ) [ x | to ]" := <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a><br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">"</span></a>''N' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astabs"><span class="id" title="definition">astabs</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">"</span></a>''N' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astabs"><span class="id" title="definition">astabs</span></a> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''N' ( S | to )") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">"</span></a>''N_' A ( S | to )" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">"</span></a>''N_' A ( S | to )" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "''N_' A ( S | to )") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">"</span></a>[ 'acts' A , 'on' S | to ]" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="abbreviation">pred_of_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">"</span></a>[ 'acts' A , 'on' S | to ]" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="abbreviation">pred_of_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'acts' A , 'on' S | to ]") : <span class="id" title="var">form_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">"</span></a>{ 'acts' A , 'on' S | to }" := (<a class="idref" href="mathcomp.fingroup.action.html#acts_on"><span class="id" title="definition">acts_on</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">"</span></a>{ 'acts' A , 'on' S | to }" := (<a class="idref" href="mathcomp.fingroup.action.html#acts_on"><span class="id" title="definition">acts_on</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "{ 'acts' A , 'on' S | to }") : <span class="id" title="var">form_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">"</span></a>[ 'transitive' A , 'on' S | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#atrans"><span class="id" title="definition">atrans</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">"</span></a>[ 'transitive' A , 'on' S | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#atrans"><span class="id" title="definition">atrans</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'transitive' A , 'on' S | to ]") : <span class="id" title="var">form_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">"</span></a>[ 'faithful' A , 'on' S | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#faithful"><span class="id" title="definition">faithful</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">"</span></a>[ 'faithful' A , 'on' S | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#faithful"><span class="id" title="definition">faithful</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'faithful' A , 'on' S | to ]") : <span class="id" title="var">form_scope</span>.<br/> <br/> @@ -348,158 +347,158 @@ <div class="code"> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RawAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="RawAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="RawAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="RawAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RawAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="RawAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="RawAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="RawAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>).<br/> <br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#RawAction.aT"><span class="id" title="variable">aT</span></a>) (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">S</span> <span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#RawAction.aT"><span class="id" title="variable">aT</span></a>) (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">S</span> <span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="act_inj"><span class="id" title="lemma">act_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#left_injective"><span class="id" title="definition">left_injective</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="act_inj"><span class="id" title="lemma">act_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_injective"><span class="id" title="definition">left_injective</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actMin"><span class="id" title="lemma">actMin</span></a> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#act_morph"><span class="id" title="definition">act_morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actMin"><span class="id" title="lemma">actMin</span></a> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#act_morph"><span class="id" title="definition">act_morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actmEfun"><span class="id" title="lemma">actmEfun</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actmEfun"><span class="id" title="lemma">actmEfun</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actmE"><span class="id" title="lemma">actmE</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actmE"><span class="id" title="lemma">actmE</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="setactE"><span class="id" title="lemma">setactE</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="setactE"><span class="id" title="lemma">setactE</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="mem_setact"><span class="id" title="lemma">mem_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="mem_setact"><span class="id" title="lemma">mem_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="card_setact"><span class="id" title="lemma">card_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_setact"><span class="id" title="lemma">card_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="setact_is_action"><span class="id" title="lemma">setact_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="setact_is_action"><span class="id" title="lemma">setact_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#setact_is_action"><span class="id" title="lemma">setact_is_action</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbitE"><span class="id" title="lemma">orbitE</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="orbitE"><span class="id" title="lemma">orbitE</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>. <br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbitP"><span class="id" title="lemma">orbitP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>).<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="mem_orbit"><span class="id" title="lemma">mem_orbit</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="mem_orbit"><span class="id" title="lemma">mem_orbit</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixP"><span class="id" title="lemma">afixP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixP"><span class="id" title="lemma">afixP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixS"><span class="id" title="lemma">afixS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixS"><span class="id" title="lemma">afixS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixU"><span class="id" title="lemma">afixU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#52f608a788da136ac97df132d7055463"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixU"><span class="id" title="lemma">afixU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix1P"><span class="id" title="lemma">afix1P</span></a> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix1P"><span class="id" title="lemma">afix1P</span></a> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">]</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabIdom"><span class="id" title="lemma">astabIdom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_D</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabIdom"><span class="id" title="lemma">astabIdom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_D</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_dom"><span class="id" title="lemma">astab_dom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_dom"><span class="id" title="lemma">astab_dom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_act"><span class="id" title="lemma">astab_act</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_act"><span class="id" title="lemma">astab_act</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabS"><span class="id" title="lemma">astabS</span></a> <span class="id" title="var">S1</span> <span class="id" title="var">S2</span> : <a class="idref" href="mathcomp.fingroup.action.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S2"><span class="id" title="variable">S2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S2"><span class="id" title="variable">S2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabS"><span class="id" title="lemma">astabS</span></a> <span class="id" title="var">S1</span> <span class="id" title="var">S2</span> : <a class="idref" href="mathcomp.fingroup.action.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S2"><span class="id" title="variable">S2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S2"><span class="id" title="variable">S2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsIdom"><span class="id" title="lemma">astabsIdom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsIdom"><span class="id" title="lemma">astabsIdom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_dom"><span class="id" title="lemma">astabs_dom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_dom"><span class="id" title="lemma">astabs_dom</span></a> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_act"><span class="id" title="lemma">astabs_act</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_act"><span class="id" title="lemma">astabs_act</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_sub"><span class="id" title="lemma">astab_sub</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_sub"><span class="id" title="lemma">astab_sub</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsC"><span class="id" title="lemma">astabsC</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#08cc1b0d2ac8db12b5c416dfc52232cc"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsC"><span class="id" title="lemma">astabsC</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsI"><span class="id" title="lemma">astabsI</span></a> <span class="id" title="var">S</span> <span class="id" title="var">T</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsI"><span class="id" title="lemma">astabsI</span></a> <span class="id" title="var">S</span> <span class="id" title="var">T</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_setact"><span class="id" title="lemma">astabs_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_setact"><span class="id" title="lemma">astabs_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1_set"><span class="id" title="lemma">astab1_set</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#set_action"><span class="id" title="definition">set_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1_set"><span class="id" title="lemma">astab1_set</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#set_action"><span class="id" title="definition">set_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_set1"><span class="id" title="lemma">astabs_set1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_set1"><span class="id" title="lemma">astabs_set1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_dom"><span class="id" title="lemma">acts_dom</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_dom"><span class="id" title="lemma">acts_dom</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_act"><span class="id" title="lemma">acts_act</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_act"><span class="id" title="lemma">acts_act</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="astabCin"><span class="id" title="lemma">astabCin</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="RawAction.ActsSetop"><span class="id" title="section">ActsSetop</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a name="RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="RawAction.ActsSetop.AactS"><span class="id" title="variable">AactS</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>) (<a name="RawAction.ActsSetop.AactT"><span class="id" title="variable">AactT</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a name="RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="RawAction.ActsSetop.AactS"><span class="id" title="variable">AactS</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>) (<a name="RawAction.ActsSetop.AactT"><span class="id" title="variable">AactT</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabU"><span class="id" title="lemma">astabU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#52f608a788da136ac97df132d7055463"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabU"><span class="id" title="lemma">astabU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsU"><span class="id" title="lemma">astabsU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#52f608a788da136ac97df132d7055463"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsU"><span class="id" title="lemma">astabsU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsD"><span class="id" title="lemma">astabsD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1db838ba797020f3b39c07ed7167bc93"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsD"><span class="id" title="lemma">astabsD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actsI"><span class="id" title="lemma">actsI</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actsI"><span class="id" title="lemma">actsI</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actsU"><span class="id" title="lemma">actsU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#52f608a788da136ac97df132d7055463"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actsU"><span class="id" title="lemma">actsU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actsD"><span class="id" title="lemma">actsD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1db838ba797020f3b39c07ed7167bc93"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actsD"><span class="id" title="lemma">actsD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.ActsSetop"><span class="id" title="section">ActsSetop</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_in_orbit"><span class="id" title="lemma">acts_in_orbit</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="subset_faithful"><span class="id" title="lemma">subset_faithful</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="RawAction.Reindex"><span class="id" title="section">Reindex</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RawAction.Reindex.vT"><span class="id" title="variable">vT</span></a> : <span class="id" title="keyword">Type</span>) (<a name="RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#vT"><span class="id" title="variable">vT</span></a>) (<a name="RawAction.Reindex.op"><span class="id" title="variable">op</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">Monoid.com_law</span></a> <a class="idref" href="mathcomp.fingroup.action.html#idx"><span class="id" title="variable">idx</span></a>) (<a name="RawAction.Reindex.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RawAction.Reindex.vT"><span class="id" title="variable">vT</span></a> : <span class="id" title="keyword">Type</span>) (<a name="RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#vT"><span class="id" title="variable">vT</span></a>) (<a name="RawAction.Reindex.op"><span class="id" title="variable">op</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">Monoid.com_law</span></a> <a class="idref" href="mathcomp.fingroup.action.html#idx"><span class="id" title="variable">idx</span></a>) (<a name="RawAction.Reindex.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="reindex_astabs"><span class="id" title="lemma">reindex_astabs</span></a> <span class="id" title="var">a</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="reindex_astabs"><span class="id" title="lemma">reindex_astabs</span></a> <span class="id" title="var">a</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="reindex_acts"><span class="id" title="lemma">reindex_acts</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#9b4515ceb280b6b5a2638c4e28ba3f31"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="reindex_acts"><span class="id" title="lemma">reindex_acts</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RawAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#RawAction.Reindex"><span class="id" title="section">Reindex</span></a>.<br/> @@ -508,16 +507,9 @@ <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#RawAction"><span class="id" title="section">RawAction</span></a>.<br/> <br/> -</div> - -<div class="doc"> - Warning: this directive depends on names of bound variables in the - definition of injective, in ssrfun.v. -</div> -<div class="code"> <br/> -<span class="id" title="keyword">Notation</span> <a name="495b9dab41eed2da7a7d91b1cb8498af"><span class="id" title="notation">"</span></a>to ^*" := (<a class="idref" href="mathcomp.fingroup.action.html#set_action"><span class="id" title="definition">set_action</span></a> <span class="id" title="var">to</span>) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="1ebbed7bbef8371b25df9685ff0f4361"><span class="id" title="notation">"</span></a>to ^*" := (<a class="idref" href="mathcomp.fingroup.action.html#set_action"><span class="id" title="definition">set_action</span></a> <span class="id" title="var">to</span>) : <span class="id" title="var">action_scope</span>.<br/> <br/> @@ -533,233 +525,233 @@ <div class="code"> <br/> -<span class="id" title="keyword">Variables</span> (<a name="PartialAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="PartialAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="PartialAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="PartialAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="PartialAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="PartialAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> <span class="id" title="keyword">Variable</span> <a name="PartialAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.rT"><span class="id" title="variable">rT</span></a>.<br/> <br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.aT"><span class="id" title="variable">aT</span></a>.<br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.rT"><span class="id" title="variable">rT</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="act1"><span class="id" title="lemma">act1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="act1"><span class="id" title="lemma">act1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actKin"><span class="id" title="lemma">actKin</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#right_loop"><span class="id" title="definition">right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actKin"><span class="id" title="lemma">actKin</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_loop"><span class="id" title="definition">right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actKVin"><span class="id" title="lemma">actKVin</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#rev_right_loop"><span class="id" title="definition">rev_right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actKVin"><span class="id" title="lemma">actKVin</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#rev_right_loop"><span class="id" title="definition">rev_right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="setactVin"><span class="id" title="lemma">setactVin</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#aa0c936d7feb8f26825e601735c0125f"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="setactVin"><span class="id" title="lemma">setactVin</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actXin"><span class="id" title="lemma">actXin</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#86a04fb564fb97d388cad84a3a204260"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actXin"><span class="id" title="lemma">actXin</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#06cdd2633d7788bac7abeac13b2dd91e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.fingroup.action.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix1"><span class="id" title="lemma">afix1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix1"><span class="id" title="lemma">afix1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixD1"><span class="id" title="lemma">afixD1</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixD1"><span class="id" title="lemma">afixD1</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_refl"><span class="id" title="lemma">orbit_refl</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_refl"><span class="id" title="lemma">orbit_refl</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="contra_orbit"><span class="id" title="lemma">contra_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="contra_orbit"><span class="id" title="lemma">contra_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_in_sym"><span class="id" title="lemma">orbit_in_sym</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#symmetric"><span class="id" title="definition">symmetric</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit_rel"><span class="id" title="abbreviation">orbit_rel</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_in_sym"><span class="id" title="lemma">orbit_in_sym</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#symmetric"><span class="id" title="definition">symmetric</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit_rel"><span class="id" title="abbreviation">orbit_rel</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_in_trans"><span class="id" title="lemma">orbit_in_trans</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#transitive"><span class="id" title="definition">transitive</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit_rel"><span class="id" title="abbreviation">orbit_rel</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_in_trans"><span class="id" title="lemma">orbit_in_trans</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#transitive"><span class="id" title="definition">transitive</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit_rel"><span class="id" title="abbreviation">orbit_rel</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_in_eqP"><span class="id" title="lemma">orbit_in_eqP</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>).<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_in_transl"><span class="id" title="lemma">orbit_in_transl</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_act_in"><span class="id" title="lemma">orbit_act_in</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">G</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_actr_in"><span class="id" title="lemma">orbit_actr_in</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">G</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_inv_in"><span class="id" title="lemma">orbit_inv_in</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_lcoset_in"><span class="id" title="lemma">orbit_lcoset_in</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7a1b86b3dd47c101ea1643c2a591eaf1"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#4df0d598fb6ea95308004f1a1fa2d9ff"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_rcoset_in"><span class="id" title="lemma">orbit_rcoset_in</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#291276ea06db0b00a2747a79d012bbe0"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#667712f80037a604c35d3cc9930cac52"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_conjsg_in"><span class="id" title="lemma">orbit_conjsg_in</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit1P"><span class="id" title="lemma">orbit1P</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit1P"><span class="id" title="lemma">orbit1P</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="card_orbit1"><span class="id" title="lemma">card_orbit1</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_orbit1"><span class="id" title="lemma">card_orbit1</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_partition"><span class="id" title="lemma">orbit_partition</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="orbit_transversal"><span class="id" title="definition">orbit_transversal</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#transversal"><span class="id" title="definition">transversal</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="orbit_transversal"><span class="id" title="definition">orbit_transversal</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#transversal"><span class="id" title="definition">transversal</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_transversalP"><span class="id" title="lemma">orbit_transversalP</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> (<span class="id" title="var">P</span> := <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>)<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_transversalP"><span class="id" title="lemma">orbit_transversalP</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> (<span class="id" title="var">P</span> := <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>)<br/> (<span class="id" title="var">X</span> := <a class="idref" href="mathcomp.fingroup.action.html#orbit_transversal"><span class="id" title="definition">orbit_transversal</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#is_transversal"><span class="id" title="definition">is_transversal</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.fingroup.action.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">&</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#is_transversal"><span class="id" title="definition">is_transversal</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.fingroup.action.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">,</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">&</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#X"><span class="id" title="variable">X</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="group_set_astab"><span class="id" title="lemma">group_set_astab</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_astab"><span class="id" title="lemma">group_set_astab</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">astab_group</span> <span class="id" title="var">S</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#group"><span class="id" title="definition">group</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#group_set_astab"><span class="id" title="lemma">group_set_astab</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix_gen_in"><span class="id" title="lemma">afix_gen_in</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation">>></span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix_gen_in"><span class="id" title="lemma">afix_gen_in</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">>></span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix_cycle_in"><span class="id" title="lemma">afix_cycle_in</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix_cycle_in"><span class="id" title="lemma">afix_cycle_in</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="afixYin"><span class="id" title="lemma">afixYin</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#80208730563aa86aa7861f6fe1b846da"><span class="id" title="notation"><*></span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0d7ccd69af81527d9facc6293603bbef"><span class="id" title="notation"><*></span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="afixMin"><span class="id" title="lemma">afixMin</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="sub_astab1_in"><span class="id" title="lemma">sub_astab1_in</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="group_set_astabs"><span class="id" title="lemma">group_set_astabs</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_astabs"><span class="id" title="lemma">group_set_astabs</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">astabs_group</span> <span class="id" title="var">S</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#group"><span class="id" title="definition">group</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#group_set_astabs"><span class="id" title="lemma">group_set_astabs</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_norm"><span class="id" title="lemma">astab_norm</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_norm"><span class="id" title="lemma">astab_norm</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_normal"><span class="id" title="lemma">astab_normal</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_normal"><span class="id" title="lemma">astab_normal</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_sub_orbit"><span class="id" title="lemma">acts_sub_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_orbit"><span class="id" title="lemma">acts_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_orbit"><span class="id" title="lemma">acts_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_subnorm_fix"><span class="id" title="lemma">acts_subnorm_fix</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_subnorm_fix"><span class="id" title="lemma">acts_subnorm_fix</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="atrans_orbit"><span class="id" title="lemma">atrans_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="atrans_orbit"><span class="id" title="lemma">atrans_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="PartialAction.OrbitStabilizer"><span class="id" title="section">OrbitStabilizer</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.rT"><span class="id" title="variable">rT</span></a>).<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="PartialAction.OrbitStabilizer.sGD"><span class="id" title="variable">sGD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.rT"><span class="id" title="variable">rT</span></a>).<br/> +<span class="id" title="keyword">Hypothesis</span> <a name="PartialAction.OrbitStabilizer.sGD"><span class="id" title="variable">sGD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a>.<br/> <span class="id" title="keyword">Let</span> <a name="PartialAction.OrbitStabilizer.ssGD"><span class="id" title="variable">ssGD</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#subsetP"><span class="id" title="lemma">subsetP</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.sGD"><span class="id" title="variable">sGD</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="amove_act"><span class="id" title="lemma">amove_act</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#291276ea06db0b00a2747a79d012bbe0"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="amove_act"><span class="id" title="lemma">amove_act</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#667712f80037a604c35d3cc9930cac52"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="amove_orbit"><span class="id" title="lemma">amove_orbit</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="amove_orbit"><span class="id" title="lemma">amove_orbit</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="amoveK"><span class="id" title="lemma">amoveK</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">Ca</span> ⇒ <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Ca"><span class="id" title="variable">Ca</span></a>))<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">Ca</span> ⇒ <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Ca"><span class="id" title="variable">Ca</span></a>))<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_stabilizer"><span class="id" title="lemma">orbit_stabilizer</span></a> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Ca"><span class="id" title="variable">Ca</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">|</span></a> <span class="id" title="var">Ca</span> <a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c4eb68ed64baca4028c54e8eaca3672a"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Ca"><span class="id" title="variable">Ca</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">|</span></a> <span class="id" title="var">Ca</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="act_reprK"><span class="id" title="lemma">act_reprK</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#1b4394c5c1740ef3dc9e4224084970bb"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#1b4394c5c1740ef3dc9e4224084970bb"><span class="id" title="notation">o</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8b4742e3f67816503ce4ab2f3b81c27e"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8b4742e3f67816503ce4ab2f3b81c27e"><span class="id" title="notation">o</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#amove"><span class="id" title="definition">amove</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer.x"><span class="id" title="variable">x</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.OrbitStabilizer"><span class="id" title="section">OrbitStabilizer</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="card_orbit_in"><span class="id" title="lemma">card_orbit_in</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_orbit_in"><span class="id" title="lemma">card_orbit_in</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="card_orbit_in_stab"><span class="id" title="lemma">card_orbit_in_stab</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_sum_card_orbit"><span class="id" title="lemma">acts_sum_card_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">(</span></a><span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">(</span></a><span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_setact_in"><span class="id" title="lemma">astab_setact_in</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_setact_in"><span class="id" title="lemma">astab_setact_in</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1_act_in"><span class="id" title="lemma">astab1_act_in</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1_act_in"><span class="id" title="lemma">astab1_act_in</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Theorem</span> <a name="Frobenius_Cauchy"><span class="id" title="lemma">Frobenius_Cauchy</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span>.<br/> +<span class="id" title="keyword">Theorem</span> <a name="Frobenius_Cauchy"><span class="id" title="lemma">Frobenius_Cauchy</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="atrans_dvd_index_in"><span class="id" title="lemma">atrans_dvd_index_in</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#aa34fd1c61c5cf0a3356b624a5d2afed"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="atrans_dvd_in"><span class="id" title="lemma">atrans_dvd_in</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#aa34fd1c61c5cf0a3356b624a5d2afed"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="atransPin"><span class="id" title="lemma">atransPin</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="atransP2in"><span class="id" title="lemma">atransP2in</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="atrans_acts_in"><span class="id" title="lemma">atrans_acts_in</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="subgroup_transitivePin"><span class="id" title="lemma">subgroup_transitivePin</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">S</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#PartialAction"><span class="id" title="section">PartialAction</span></a>.<br/> @@ -767,16 +759,16 @@ <br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">"</span></a>''C' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astab_group"><span class="id" title="definition">astab_group</span></a> <span class="id" title="var">to</span> <span class="id" title="var">S</span>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="604222e4f2ad6aacb5fe189ffe7e1dce"><span class="id" title="notation">"</span></a>''C_' A ( S | to )" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">)</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="5b118df1249ebe77f4eea4d7d4bb73a3"><span class="id" title="notation">"</span></a>''C_' ( A ) ( S | to )" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">"</span></a>''C' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astab_group"><span class="id" title="definition">astab_group</span></a> <span class="id" title="var">to</span> <span class="id" title="var">S</span>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="730b86160be8ee244fee3d51d1461c62"><span class="id" title="notation">"</span></a>''C_' A ( S | to )" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">)</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="6c61b26ccba3b91a53eca9c0e2704b4b"><span class="id" title="notation">"</span></a>''C_' ( A ) ( S | to )" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">"</span></a>''C' [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#astab_group"><span class="id" title="definition">astab_group</span></a> <span class="id" title="var">to</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span>%<span class="id" title="var">g</span><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="619a9997befee6604ab4a6637eedd029"><span class="id" title="notation">"</span></a>''C_' A [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="ecd380e2cecb617207c50384383b0bc7"><span class="id" title="notation">"</span></a>''C_' ( A ) [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#01e2893fcf35e18b1e93a5c4b5f16e1c"><span class="id" title="notation">]</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">"</span></a>''C' [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.action.html#astab_group"><span class="id" title="definition">astab_group</span></a> <span class="id" title="var">to</span> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span>%<span class="id" title="var">g</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="d7638015275b7b311b1925f758e3eeb6"><span class="id" title="notation">"</span></a>''C_' A [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="0c44862d5f7bd548d0954bd02a085d07"><span class="id" title="notation">"</span></a>''C_' ( A ) [ x | to ]" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">[</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#08d2d1cc311a7330e42dada64b6f2b61"><span class="id" title="notation">]</span></a>)<br/> (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d8a7e9dd3de10046d82874af3a1cdeb8"><span class="id" title="notation">"</span></a>''N' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astabs_group"><span class="id" title="definition">astabs_group</span></a> <span class="id" title="var">to</span> <span class="id" title="var">S</span>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="dd7f1c8bab5f82c80672e99d9005640a"><span class="id" title="notation">"</span></a>''N_' A ( S | to )" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#d8a7e9dd3de10046d82874af3a1cdeb8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d8a7e9dd3de10046d82874af3a1cdeb8"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#d8a7e9dd3de10046d82874af3a1cdeb8"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#d8a7e9dd3de10046d82874af3a1cdeb8"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#d8a7e9dd3de10046d82874af3a1cdeb8"><span class="id" title="notation">)</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="d9c5bdc15a858bbafd592cb0ddbccd5a"><span class="id" title="notation">"</span></a>''N' ( S | to )" := (<a class="idref" href="mathcomp.fingroup.action.html#astabs_group"><span class="id" title="definition">astabs_group</span></a> <span class="id" title="var">to</span> <span class="id" title="var">S</span>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="f9336d4fef640b2e2bd519987a56f884"><span class="id" title="notation">"</span></a>''N_' A ( S | to )" := (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.fingroup.action.html#d9c5bdc15a858bbafd592cb0ddbccd5a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9c5bdc15a858bbafd592cb0ddbccd5a"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9c5bdc15a858bbafd592cb0ddbccd5a"><span class="id" title="notation">(</span></a><span class="id" title="var">S</span> <a class="idref" href="mathcomp.fingroup.action.html#d9c5bdc15a858bbafd592cb0ddbccd5a"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#d9c5bdc15a858bbafd592cb0ddbccd5a"><span class="id" title="notation">)</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="TotalActions"><span class="id" title="section">TotalActions</span></a>.<br/> @@ -791,139 +783,139 @@ <span class="id" title="keyword">Variable</span> (<a name="TotalActions.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="TotalActions.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="TotalActions.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">&-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="TotalActions.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#5567a34191268487a9ef0120f668a04c"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5567a34191268487a9ef0120f668a04c"><span class="id" title="notation">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5567a34191268487a9ef0120f668a04c"><span class="id" title="notation">&-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.action.html#5567a34191268487a9ef0120f668a04c"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a>) (<span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a>) (<span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actM"><span class="id" title="lemma">actM</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actM"><span class="id" title="lemma">actM</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actK"><span class="id" title="lemma">actK</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#right_loop"><span class="id" title="definition">right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actK"><span class="id" title="lemma">actK</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_loop"><span class="id" title="definition">right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actKV"><span class="id" title="lemma">actKV</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#rev_right_loop"><span class="id" title="definition">rev_right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actKV"><span class="id" title="lemma">actKV</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#rev_right_loop"><span class="id" title="definition">rev_right_loop</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#invg"><span class="id" title="definition">invg</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actX"><span class="id" title="lemma">actX</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">n</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#86a04fb564fb97d388cad84a3a204260"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.fingroup.action.html#n"><span class="id" title="variable">n</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.fingroup.action.html#n"><span class="id" title="variable">n</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actX"><span class="id" title="lemma">actX</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">n</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#06cdd2633d7788bac7abeac13b2dd91e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.fingroup.action.html#n"><span class="id" title="variable">n</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.fingroup.action.html#n"><span class="id" title="variable">n</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actCJ"><span class="id" title="lemma">actCJ</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#808c6b8e35e792f23899f360a21e4638"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="actCJ"><span class="id" title="lemma">actCJ</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actCJV"><span class="id" title="lemma">actCJV</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#808c6b8e35e792f23899f360a21e4638"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a>)) <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actCJV"><span class="id" title="lemma">actCJV</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a>)) <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_sym"><span class="id" title="lemma">orbit_sym</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_sym"><span class="id" title="lemma">orbit_sym</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_trans"><span class="id" title="lemma">orbit_trans</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_eqP"><span class="id" title="lemma">orbit_eqP</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>).<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_transl"><span class="id" title="lemma">orbit_transl</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_act"><span class="id" title="lemma">orbit_act</span></a> <span class="id" title="var">G</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span>: <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_act"><span class="id" title="lemma">orbit_act</span></a> <span class="id" title="var">G</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span>: <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_actr"><span class="id" title="lemma">orbit_actr</span></a> <span class="id" title="var">G</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_eq_mem"><span class="id" title="lemma">orbit_eq_mem</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_inv"><span class="id" title="lemma">orbit_inv</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_inv"><span class="id" title="lemma">orbit_inv</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_lcoset"><span class="id" title="lemma">orbit_lcoset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7a1b86b3dd47c101ea1643c2a591eaf1"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_lcoset"><span class="id" title="lemma">orbit_lcoset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#4df0d598fb6ea95308004f1a1fa2d9ff"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_rcoset"><span class="id" title="lemma">orbit_rcoset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#291276ea06db0b00a2747a79d012bbe0"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#667712f80037a604c35d3cc9930cac52"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="orbit_conjsg"><span class="id" title="lemma">orbit_conjsg</span></a> <span class="id" title="var">A</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabP"><span class="id" title="lemma">astabP</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabP"><span class="id" title="lemma">astabP</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1P"><span class="id" title="lemma">astab1P</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1P"><span class="id" title="lemma">astab1P</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_astab1"><span class="id" title="lemma">sub_astab1</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="sub_astab1"><span class="id" title="lemma">sub_astab1</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabC"><span class="id" title="lemma">astabC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabC"><span class="id" title="lemma">astabC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix_cycle"><span class="id" title="lemma">afix_cycle</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix_cycle"><span class="id" title="lemma">afix_cycle</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#2f26cd6b59b1ae1fb2356f20ddb57cf1"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix_gen"><span class="id" title="lemma">afix_gen</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation">>></span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix_gen"><span class="id" title="lemma">afix_gen</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">>></span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixM"><span class="id" title="lemma">afixM</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixM"><span class="id" title="lemma">afixM</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="astabsP"><span class="id" title="lemma">astabsP</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>).<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="card_orbit"><span class="id" title="lemma">card_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_orbit"><span class="id" title="lemma">card_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="dvdn_orbit"><span class="id" title="lemma">dvdn_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#aa34fd1c61c5cf0a3356b624a5d2afed"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="dvdn_orbit"><span class="id" title="lemma">dvdn_orbit</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="card_orbit_stab"><span class="id" title="lemma">card_orbit_stab</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : (<a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_orbit_stab"><span class="id" title="lemma">card_orbit_stab</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : (<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actsP"><span class="id" title="lemma">actsP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actsP"><span class="id" title="lemma">actsP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="setact_orbit"><span class="id" title="lemma">setact_orbit</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="setact_orbit"><span class="id" title="lemma">setact_orbit</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_setact"><span class="id" title="lemma">astab_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_setact"><span class="id" title="lemma">astab_setact</span></a> <span class="id" title="var">S</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1_act"><span class="id" title="lemma">astab1_act</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1_act"><span class="id" title="lemma">astab1_act</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="atransP"><span class="id" title="lemma">atransP</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="atransP"><span class="id" title="lemma">atransP</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="atransP2"><span class="id" title="lemma">atransP2</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="atransP2"><span class="id" title="lemma">atransP2</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">a</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="atrans_acts"><span class="id" title="lemma">atrans_acts</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="atrans_acts"><span class="id" title="lemma">atrans_acts</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="atrans_supgroup"><span class="id" title="lemma">atrans_supgroup</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="atrans_acts_card"><span class="id" title="lemma">atrans_acts_card</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 1%<span class="id" title="var">N</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1%<span class="id" title="var">N</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="atrans_dvd"><span class="id" title="lemma">atrans_dvd</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#aa34fd1c61c5cf0a3356b624a5d2afed"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="atrans_dvd"><span class="id" title="lemma">atrans_dvd</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> </div> @@ -932,12 +924,12 @@ This is Aschbacher (5.2) </div> <div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="acts_fix_norm"><span class="id" title="lemma">acts_fix_norm</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_fix_norm"><span class="id" title="lemma">acts_fix_norm</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="faithfulP"><span class="id" title="lemma">faithfulP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1)<br/> - <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1)<br/> + <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a>.<br/> <br/> </div> @@ -947,7 +939,7 @@ </div> <div class="code"> <span class="id" title="keyword">Lemma</span> <a name="astab_trans_gcore"><span class="id" title="lemma">astab_trans_gcore</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> <span class="id" title="var">u</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#gcore"><span class="id" title="definition">gcore</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#gcore"><span class="id" title="definition">gcore</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> <br/> </div> @@ -957,8 +949,8 @@ </div> <div class="code"> <span class="id" title="keyword">Theorem</span> <a name="subgroup_transitiveP"><span class="id" title="lemma">subgroup_transitiveP</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">S</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a>.<br/> <br/> </div> @@ -968,9 +960,9 @@ </div> <div class="code"> <span class="id" title="keyword">Lemma</span> <a name="trans_subnorm_fixP"><span class="id" title="lemma">trans_subnorm_fixP</span></a> <span class="id" title="var">x</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">S</span> :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">C</span> := <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d6d8c6555a0082b6cbf651a274d2a4d6"><span class="id" title="notation">]</span></a> <span class="id" title="tactic">in</span> <span class="id" title="keyword">let</span> <span class="id" title="var">T</span> := <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#2dab1b186f22df1296e4090457f5abb0"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#6c121d1bcff5b1c0972474f398d18325"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#2dab1b186f22df1296e4090457f5abb0"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#2dab1b186f22df1296e4090457f5abb0"><span class="id" title="notation">::&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#6c121d1bcff5b1c0972474f398d18325"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a>.<br/> + <span class="id" title="keyword">let</span> <span class="id" title="var">C</span> := <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#395ebe95a73fc3c95c78bb1b65adcef4"><span class="id" title="notation">]</span></a> <span class="id" title="tactic">in</span> <span class="id" title="keyword">let</span> <span class="id" title="var">T</span> := <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a> <span class="id" title="tactic">in</span><br/> + <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#7ed77f64965385480255328de15d774c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#9034a9c14f90b74fd311ece73a2afd4b"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#7ed77f64965385480255328de15d774c"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#7ed77f64965385480255328de15d774c"><span class="id" title="notation">::&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#9034a9c14f90b74fd311ece73a2afd4b"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#TotalActions"><span class="id" title="section">TotalActions</span></a>.<br/> @@ -981,14 +973,14 @@ <span class="id" title="keyword">Section</span> <a name="Restrict"><span class="id" title="section">Restrict</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="Restrict.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="Restrict.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="Restrict.rT"><span class="id" title="variable">rT</span></a> : <span class="id" title="keyword">Type</span>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="Restrict.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.rT"><span class="id" title="variable">rT</span></a>) (<a name="Restrict.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="Restrict.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="Restrict.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="Restrict.rT"><span class="id" title="variable">rT</span></a> : <span class="id" title="keyword">Type</span>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="Restrict.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.rT"><span class="id" title="variable">rT</span></a>) (<a name="Restrict.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="ract"><span class="id" title="definition">ract</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.D"><span class="id" title="variable">D</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="projection">act</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.to"><span class="id" title="variable">to</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="ract"><span class="id" title="definition">ract</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.D"><span class="id" title="variable">D</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="projection">act</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.to"><span class="id" title="variable">to</span></a>.<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="Restrict.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#Restrict.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.D"><span class="id" title="variable">D</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="Restrict.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#Restrict.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.D"><span class="id" title="variable">D</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="ract_is_action"><span class="id" title="lemma">ract_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.A"><span class="id" title="variable">A</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#ract"><span class="id" title="definition">ract</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.sAD"><span class="id" title="variable">sAD</span></a>).<br/> @@ -997,7 +989,7 @@ <span class="id" title="keyword">Canonical</span> <span class="id" title="var">raction</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ract_is_action"><span class="id" title="lemma">ract_is_action</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="ractE"><span class="id" title="lemma">ractE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#raction"><span class="id" title="definition">raction</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.to"><span class="id" title="variable">to</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="ractE"><span class="id" title="lemma">ractE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#raction"><span class="id" title="definition">raction</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Restrict.to"><span class="id" title="variable">to</span></a>. <br/> <br/> </div> @@ -1012,24 +1004,24 @@ <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#Restrict"><span class="id" title="section">Restrict</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">"</span></a>to \ sAD" := (<a class="idref" href="mathcomp.fingroup.action.html#raction"><span class="id" title="definition">raction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">sAD</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">"</span></a>to \ sAD" := (<a class="idref" href="mathcomp.fingroup.action.html#raction"><span class="id" title="definition">raction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">sAD</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50) : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="ActBy"><span class="id" title="section">ActBy</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="ActBy.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActBy.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="ActBy.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="ActBy.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActBy.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="ActBy.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="actby_cond"><span class="id" title="definition">actby_cond</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) <span class="id" title="var">R</span> (<span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.rT"><span class="id" title="variable">rT</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="actby_cond"><span class="id" title="definition">actby_cond</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">R</span> (<span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.rT"><span class="id" title="variable">rT</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="actby"><span class="id" title="definition">actby</span></a> <span class="id" title="var">A</span> <span class="id" title="var">R</span> <span class="id" title="var">to</span> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.fingroup.action.html#actby_cond"><span class="id" title="definition">actby_cond</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> :=<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> + <span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="ActBy.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="ActBy.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="ActBy.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.rT"><span class="id" title="variable">rT</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="ActBy.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="ActBy.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="ActBy.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.rT"><span class="id" title="variable">rT</span></a>).<br/> <span class="id" title="keyword">Hypothesis</span> <a name="ActBy.nRA"><span class="id" title="variable">nRA</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#actby_cond"><span class="id" title="definition">actby_cond</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a>.<br/> <br/> @@ -1039,52 +1031,52 @@ <span class="id" title="keyword">Canonical</span> <span class="id" title="var">action_by</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actby_is_action"><span class="id" title="lemma">actby_is_action</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actbyE"><span class="id" title="lemma">actbyE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">]></span></a>%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actbyE"><span class="id" title="lemma">actbyE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">]></span></a>%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix_actby"><span class="id" title="lemma">afix_actby</span></a> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#08cc1b0d2ac8db12b5c416dfc52232cc"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#52f608a788da136ac97df132d7055463"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ActBy.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix_actby"><span class="id" title="lemma">afix_actby</span></a> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ActBy.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_actby"><span class="id" title="lemma">astab_actby</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_actby"><span class="id" title="lemma">astab_actby</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_actby"><span class="id" title="lemma">astabs_actby</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_actby"><span class="id" title="lemma">astabs_actby</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_actby"><span class="id" title="lemma">acts_actby</span></a> (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#5bf4be35f60d187d626f827a16d8a344"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_actby"><span class="id" title="lemma">acts_actby</span></a> (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">S</span> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">nRA</span></a><a class="idref" href="mathcomp.fingroup.action.html#6cb933d23b4e1104f17518736b51639e"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActBy.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#ActBy"><span class="id" title="section">ActBy</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation">"</span></a><[ nRA ] >" := (<a class="idref" href="mathcomp.fingroup.action.html#action_by"><span class="id" title="definition">action_by</span></a> <span class="id" title="var">nRA</span>) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation">"</span></a><[ nRA ] >" := (<a class="idref" href="mathcomp.fingroup.action.html#action_by"><span class="id" title="definition">action_by</span></a> <span class="id" title="var">nRA</span>) : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="SubAction"><span class="id" title="section">SubAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="SubAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="SubAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="SubAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="SubAction.sP"><span class="id" title="variable">sP</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>) (<a name="SubAction.sT"><span class="id" title="variable">sT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#subFinType"><span class="id" title="record">subFinType</span></a> <a class="idref" href="mathcomp.fingroup.action.html#sP"><span class="id" title="variable">sP</span></a>) (<a name="SubAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="SubAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="SubAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="SubAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="SubAction.sP"><span class="id" title="variable">sP</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>) (<a name="SubAction.sT"><span class="id" title="variable">sT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#subFinType"><span class="id" title="record">subFinType</span></a> <a class="idref" href="mathcomp.fingroup.action.html#sP"><span class="id" title="variable">sP</span></a>) (<a name="SubAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a>).<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.fingroup.action.html#SubAction.sT"><span class="id" title="variable">sT</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.sT"><span class="id" title="variable">sT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.sT"><span class="id" title="variable">sT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="subact_dom"><span class="id" title="definition">subact_dom</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.sP"><span class="id" title="variable">sP</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">subact_dom_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="subact_dom"><span class="id" title="definition">subact_dom</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.sP"><span class="id" title="variable">sP</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">subact_dom_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">Na</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">{</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">Na</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">{</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">}</span></a>.<br/> <span class="id" title="keyword">Lemma</span> <a name="sub_act_proof"><span class="id" title="lemma">sub_act_proof</span></a> <span class="id" title="var">u</span> <span class="id" title="var">Na</span> : <a class="idref" href="mathcomp.fingroup.action.html#SubAction.sP"><span class="id" title="variable">sP</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a>) (<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Na"><span class="id" title="variable">Na</span></a>)).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="subact"><span class="id" title="definition">subact</span></a> <span class="id" title="var">u</span> <span class="id" title="var">a</span> :=<br/> - <span class="id" title="keyword">if</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <span class="id" title="keyword">is</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <span class="id" title="var">Na</span> <span class="id" title="keyword">then</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <span class="id" title="var">_</span> (<a class="idref" href="mathcomp.fingroup.action.html#sub_act_proof"><span class="id" title="lemma">sub_act_proof</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <span class="id" title="var">Na</span>) <span class="id" title="keyword">else</span> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a>.<br/> + <span class="id" title="keyword">if</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <span class="id" title="keyword">is</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <span class="id" title="var">Na</span> <span class="id" title="keyword">then</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <span class="id" title="var">_</span> (<a class="idref" href="mathcomp.fingroup.action.html#sub_act_proof"><span class="id" title="lemma">sub_act_proof</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <span class="id" title="var">Na</span>) <span class="id" title="keyword">else</span> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="val_subact"><span class="id" title="lemma">val_subact</span></a> <span class="id" title="var">u</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#subact"><span class="id" title="definition">subact</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a>.<br/> + <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#subact"><span class="id" title="definition">subact</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.fingroup.action.html#u"><span class="id" title="variable">u</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="subact_is_action"><span class="id" title="lemma">subact_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact"><span class="id" title="definition">subact</span></a>.<br/> @@ -1093,102 +1085,102 @@ <span class="id" title="keyword">Canonical</span> <span class="id" title="var">subaction</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_is_action"><span class="id" title="lemma">subact_is_action</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_subact"><span class="id" title="lemma">astab_subact</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subaction"><span class="id" title="definition">subaction</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_subact"><span class="id" title="lemma">astab_subact</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subaction"><span class="id" title="definition">subaction</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_subact"><span class="id" title="lemma">astabs_subact</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subaction"><span class="id" title="definition">subaction</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_subact"><span class="id" title="lemma">astabs_subact</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subaction"><span class="id" title="definition">subaction</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#SubAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="afix_subact"><span class="id" title="lemma">afix_subact</span></a> <span class="id" title="var">A</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_subaction</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#aa0c936d7feb8f26825e601735c0125f"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subact_dom"><span class="id" title="definition">subact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_subaction</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#SubAction"><span class="id" title="section">SubAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="d0c9249f50b96ff03ab4b012119ece66"><span class="id" title="notation">"</span></a>to ^?" := (<a class="idref" href="mathcomp.fingroup.action.html#subaction"><span class="id" title="definition">subaction</span></a> <span class="id" title="var">_</span> <span class="id" title="var">to</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="fd4561b297ac1486385871066c674507"><span class="id" title="notation">"</span></a>to ^?" := (<a class="idref" href="mathcomp.fingroup.action.html#subaction"><span class="id" title="definition">subaction</span></a> <span class="id" title="var">_</span> <span class="id" title="var">to</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "to ^?") : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="QuotientAction"><span class="id" title="section">QuotientAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="QuotientAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="QuotientAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="QuotientAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="QuotientAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a>) (<a name="QuotientAction.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="QuotientAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="QuotientAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="QuotientAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="QuotientAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a>) (<a name="QuotientAction.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="qact_dom"><span class="id" title="definition">qact_dom</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#495b9dab41eed2da7a7d91b1cb8498af"><span class="id" title="notation">^*</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">qact_dom_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ccb763a84253e971fd106aeeb9cd3cb0"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="qact_dom"><span class="id" title="definition">qact_dom</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#1ebbed7bbef8371b25df9685ff0f4361"><span class="id" title="notation">^*</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">qact_dom_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f6996ff347e6cf832aa130837b06a848"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Fact</span> <a name="qact_subdomE"><span class="id" title="lemma">qact_subdomE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#subdom"><span class="id" title="abbreviation">subdom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a>.<br/> - <span class="id" title="keyword">Lemma</span> <a name="qact_proof"><span class="id" title="lemma">qact_proof</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subdom"><span class="id" title="abbreviation">subdom</span></a>.<br/> +<span class="id" title="keyword">Fact</span> <a name="qact_subdomE"><span class="id" title="lemma">qact_subdomE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#subdom"><span class="id" title="abbreviation">subdom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a>.<br/> + <span class="id" title="keyword">Lemma</span> <a name="qact_proof"><span class="id" title="lemma">qact_proof</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#subdom"><span class="id" title="abbreviation">subdom</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="qact"><span class="id" title="definition">qact</span></a> : <a class="idref" href="mathcomp.fingroup.quotient.html#coset_of"><span class="id" title="record">coset_of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset_of"><span class="id" title="record">coset_of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="projection">act</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#495b9dab41eed2da7a7d91b1cb8498af"><span class="id" title="notation">^*</span></a><a class="idref" href="mathcomp.fingroup.action.html#d0c9249f50b96ff03ab4b012119ece66"><span class="id" title="notation">^?</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_proof"><span class="id" title="lemma">qact_proof</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="qact"><span class="id" title="definition">qact</span></a> : <a class="idref" href="mathcomp.fingroup.quotient.html#coset_of"><span class="id" title="record">coset_of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset_of"><span class="id" title="record">coset_of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="projection">act</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#1ebbed7bbef8371b25df9685ff0f4361"><span class="id" title="notation">^*</span></a><a class="idref" href="mathcomp.fingroup.action.html#fd4561b297ac1486385871066c674507"><span class="id" title="notation">^?</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_proof"><span class="id" title="lemma">qact_proof</span></a>).<br/> <br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">quotient_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact"><span class="id" title="definition">qact</span></a><a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">quotient_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact"><span class="id" title="definition">qact</span></a><a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_qact_dom"><span class="id" title="lemma">acts_qact_dom</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_qact_dom"><span class="id" title="lemma">acts_qact_dom</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="qactEcond"><span class="id" title="lemma">qactEcond</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> <a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>).<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="qactE"><span class="id" title="lemma">qactE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> + <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_quotient"><span class="id" title="lemma">acts_quotient</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">N_qact_dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_quotient"><span class="id" title="lemma">acts_quotient</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">N_qact_dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_quotient"><span class="id" title="lemma">astabs_quotient</span></a> (<span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">N_qact_dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_quotient"><span class="id" title="lemma">astabs_quotient</span></a> (<span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">N_qact_dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#QuotientAction"><span class="id" title="section">QuotientAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="2e4ccc4d97341df4136dd243a5fe1a5c"><span class="id" title="notation">"</span></a>to / H" := (<a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="ad04e00ef26e546e5433da83c9f70dee"><span class="id" title="notation">"</span></a>to / H" := (<a class="idref" href="mathcomp.fingroup.action.html#quotient_action"><span class="id" title="definition">quotient_action</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="ModAction"><span class="id" title="section">ModAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="ModAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ModAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="ModAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="ModAction.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ModAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="ModAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> <span class="id" title="keyword">Variable</span> <a name="ModAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.rT"><span class="id" title="variable">rT</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> <span class="id" title="keyword">Section</span> <a name="ModAction.GenericMod"><span class="id" title="section">GenericMod</span></a>.<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Let</span> <a name="ModAction.GenericMod.acts_dom"><span class="id" title="variable">acts_dom</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#dom"><span class="id" title="abbreviation">dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">}</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#acts_act"><span class="id" title="lemma">acts_act</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#acts_subnorm_fix"><span class="id" title="lemma">acts_subnorm_fix</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>).<br/> +<span class="id" title="keyword">Let</span> <a name="ModAction.GenericMod.acts_dom"><span class="id" title="variable">acts_dom</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#dom"><span class="id" title="abbreviation">dom</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">}</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#acts_act"><span class="id" title="lemma">acts_act</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#acts_subnorm_fix"><span class="id" title="lemma">acts_subnorm_fix</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="modact"><span class="id" title="definition">modact</span></a> <span class="id" title="var">x</span> (<span class="id" title="var">Ha</span> : <a class="idref" href="mathcomp.fingroup.quotient.html#coset_of"><span class="id" title="record">coset_of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>) :=<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Ha"><span class="id" title="variable">Ha</span></a>)) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Ha"><span class="id" title="variable">Ha</span></a>)) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="modactEcond"><span class="id" title="lemma">modactEcond</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#dom"><span class="id" title="abbreviation">dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#modact"><span class="id" title="definition">modact</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#dom"><span class="id" title="abbreviation">dom</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#modact"><span class="id" title="definition">modact</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="modactE"><span class="id" title="lemma">modactE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#modact"><span class="id" title="definition">modact</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#range"><span class="id" title="abbreviation">range</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#modact"><span class="id" title="definition">modact</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="modact_is_action"><span class="id" title="lemma">modact_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#modact"><span class="id" title="definition">modact</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="modact_is_action"><span class="id" title="lemma">modact_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#modact"><span class="id" title="definition">modact</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">mod_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#modact_is_action"><span class="id" title="lemma">modact_is_action</span></a>.<br/> @@ -1197,38 +1189,38 @@ <span class="id" title="keyword">Section</span> <a name="ModAction.GenericMod.Stabilizers"><span class="id" title="section">Stabilizers</span></a>.<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="ModAction.GenericMod.Stabilizers.cSH"><span class="id" title="variable">cSH</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Hypothesis</span> <a name="ModAction.GenericMod.Stabilizers.cSH"><span class="id" title="variable">cSH</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Let</span> <a name="ModAction.GenericMod.Stabilizers.fixSH"><span class="id" title="variable">fixSH</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Let</span> <a name="ModAction.GenericMod.Stabilizers.fixSH"><span class="id" title="variable">fixSH</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_mod"><span class="id" title="lemma">astabs_mod</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_mod"><span class="id" title="lemma">astabs_mod</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_mod"><span class="id" title="lemma">astab_mod</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_mod"><span class="id" title="lemma">astab_mod</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.Stabilizers"><span class="id" title="section">Stabilizers</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="afix_mod"><span class="id" title="lemma">afix_mod</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.GenericMod"><span class="id" title="section">GenericMod</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="modact_faithful"><span class="id" title="lemma">modact_faithful</span></a> <span class="id" title="var">G</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#604222e4f2ad6aacb5fe189ffe7e1dce"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#604222e4f2ad6aacb5fe189ffe7e1dce"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#604222e4f2ad6aacb5fe189ffe7e1dce"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#604222e4f2ad6aacb5fe189ffe7e1dce"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#604222e4f2ad6aacb5fe189ffe7e1dce"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#730b86160be8ee244fee3d51d1461c62"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#730b86160be8ee244fee3d51d1461c62"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#730b86160be8ee244fee3d51d1461c62"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#730b86160be8ee244fee3d51d1461c62"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ModAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#730b86160be8ee244fee3d51d1461c62"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#ModAction"><span class="id" title="section">ModAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="2763ae1d41d6f4b536ed07b20d50de88"><span class="id" title="notation">"</span></a>to %% H" := (<a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="a31739c14704f62c7a05474f0d8f2ec1"><span class="id" title="notation">"</span></a>to %% H" := (<a class="idref" href="mathcomp.fingroup.action.html#mod_action"><span class="id" title="definition">mod_action</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="ActPerm"><span class="id" title="section">ActPerm</span></a>.<br/> @@ -1240,26 +1232,26 @@ <div class="code"> <br/> -<span class="id" title="keyword">Variables</span> (<a name="ActPerm.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActPerm.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="ActPerm.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="ActPerm.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActPerm.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="ActPerm.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> <span class="id" title="keyword">Variable</span> <a name="ActPerm.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.rT"><span class="id" title="variable">rT</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="actperm"><span class="id" title="definition">actperm</span></a> <span class="id" title="var">a</span> := <a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#act_inj"><span class="id" title="lemma">act_inj</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actpermM"><span class="id" title="lemma">actpermM</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">:</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actpermM"><span class="id" title="lemma">actpermM</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">:</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">actperm_morphism</span> := <a class="idref" href="mathcomp.fingroup.morphism.html#Morphism"><span class="id" title="constructor">Morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actpermM"><span class="id" title="lemma">actpermM</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actpermE"><span class="id" title="lemma">actpermE</span></a> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actpermE"><span class="id" title="lemma">actpermE</span></a> <span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actpermK"><span class="id" title="lemma">actpermK</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.perm.html#aperm"><span class="id" title="definition">aperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actpermK"><span class="id" title="lemma">actpermK</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.perm.html#aperm"><span class="id" title="definition">aperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="ker_actperm"><span class="id" title="lemma">ker_actperm</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#034cc0eb573e9a86d9574eaed7b27a13"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#034cc0eb573e9a86d9574eaed7b27a13"><span class="id" title="notation">ker</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="ker_actperm"><span class="id" title="lemma">ker_actperm</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#7ef99623452370540bbc44fd30b0bc94"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#7ef99623452370540bbc44fd30b0bc94"><span class="id" title="notation">ker</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#ActPerm"><span class="id" title="section">ActPerm</span></a>.<br/> @@ -1268,31 +1260,31 @@ <span class="id" title="keyword">Section</span> <a name="RestrictActionTheory"><span class="id" title="section">RestrictActionTheory</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="RestrictActionTheory.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="RestrictActionTheory.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="RestrictActionTheory.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="RestrictActionTheory.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> <span class="id" title="keyword">Variables</span> (<a name="RestrictActionTheory.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.rT"><span class="id" title="variable">rT</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="faithful_isom"><span class="id" title="lemma">faithful_isom</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) <span class="id" title="var">S</span> (<span class="id" title="var">nSA</span> : <a class="idref" href="mathcomp.fingroup.action.html#actby_cond"><span class="id" title="definition">actby_cond</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#nSA"><span class="id" title="variable">nSA</span></a><a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation">]></span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#nSA"><span class="id" title="variable">nSA</span></a><a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation">]></span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="faithful_isom"><span class="id" title="lemma">faithful_isom</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) <span class="id" title="var">S</span> (<span class="id" title="var">nSA</span> : <a class="idref" href="mathcomp.fingroup.action.html#actby_cond"><span class="id" title="definition">actby_cond</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a>) :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#nSA"><span class="id" title="variable">nSA</span></a><a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation">]></span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#nSA"><span class="id" title="variable">nSA</span></a><a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation">]></span></a>).<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RestrictActionTheory.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.D"><span class="id" title="variable">D</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RestrictActionTheory.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.D"><span class="id" title="variable">D</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="ractpermE"><span class="id" title="lemma">ractpermE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="ractpermE"><span class="id" title="lemma">ractpermE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix_ract"><span class="id" title="lemma">afix_ract</span></a> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="afix_ract"><span class="id" title="lemma">afix_ract</span></a> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_ract"><span class="id" title="lemma">astab_ract</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_ract"><span class="id" title="lemma">astab_ract</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_ract"><span class="id" title="lemma">astabs_ract</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_ract"><span class="id" title="lemma">astabs_ract</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_ract"><span class="id" title="lemma">acts_ract</span></a> (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_ract"><span class="id" title="lemma">acts_ract</span></a> (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">S</span> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.sAD"><span class="id" title="variable">sAD</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#RestrictActionTheory"><span class="id" title="section">RestrictActionTheory</span></a>.<br/> @@ -1307,8 +1299,8 @@ <div class="code"> <br/> -<span class="id" title="keyword">Variables</span> (<a name="MorphAct.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="MorphAct.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="MorphAct.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> -<span class="id" title="keyword">Variable</span> <a name="MorphAct.phi"><span class="id" title="variable">phi</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="MorphAct.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="MorphAct.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="MorphAct.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> +<span class="id" title="keyword">Variable</span> <a name="MorphAct.phi"><span class="id" title="variable">phi</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.perm.html#683bed2e43e8b9b52492c89e618e34b6"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#683bed2e43e8b9b52492c89e618e34b6"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.perm.html#683bed2e43e8b9b52492c89e618e34b6"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="mact"><span class="id" title="definition">mact</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> := <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> @@ -1320,51 +1312,51 @@ <span class="id" title="keyword">Canonical</span> <span class="id" title="var">morph_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mact_is_action"><span class="id" title="lemma">mact_is_action</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="mactE"><span class="id" title="lemma">mactE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="mactE"><span class="id" title="lemma">mactE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="injm_faithful"><span class="id" title="lemma">injm_faithful</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="injm_faithful"><span class="id" title="lemma">injm_faithful</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="perm_mact"><span class="id" title="lemma">perm_mact</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="perm_mact"><span class="id" title="lemma">perm_mact</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct.phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#MorphAct"><span class="id" title="section">MorphAct</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="157b1d4873eeace33ab3d1b9523d7613"><span class="id" title="notation">"</span></a><< phi >>" := (<a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a> <span class="id" title="var">phi</span>) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="c689c05cedec45f82cf37dc613a5bc23"><span class="id" title="notation">"</span></a><< phi >>" := (<a class="idref" href="mathcomp.fingroup.action.html#morph_action"><span class="id" title="definition">morph_action</span></a> <span class="id" title="var">phi</span>) : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="CompAct"><span class="id" title="section">CompAct</span></a>.<br/> <br/> <span class="id" title="keyword">Variables</span> (<a name="CompAct.gT"><span class="id" title="variable">gT</span></a> <a name="CompAct.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="CompAct.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="CompAct.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="CompAct.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.rT"><span class="id" title="variable">rT</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="CompAct.B"><span class="id" title="variable">B</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="CompAct.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="CompAct.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="CompAct.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.rT"><span class="id" title="variable">rT</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="CompAct.B"><span class="id" title="variable">B</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="CompAct.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="comp_act"><span class="id" title="definition">comp_act</span></a> <span class="id" title="var">x</span> <span class="id" title="var">e</span> := <a class="idref" href="mathcomp.fingroup.action.html#CompAct.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e"><span class="id" title="variable">e</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="comp_is_action"><span class="id" title="lemma">comp_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#619a2190d60a66179f3396458e2a09ae"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.D"><span class="id" title="variable">D</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#comp_act"><span class="id" title="definition">comp_act</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="comp_is_action"><span class="id" title="lemma">comp_is_action</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_action"><span class="id" title="definition">is_action</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#320f70d30c9a649ec82642b364681418"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.D"><span class="id" title="variable">D</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#comp_act"><span class="id" title="definition">comp_act</span></a>.<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">comp_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#comp_is_action"><span class="id" title="lemma">comp_is_action</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="comp_actE"><span class="id" title="lemma">comp_actE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">e</span> : <a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e"><span class="id" title="variable">e</span></a>). <br/> +<span class="id" title="keyword">Lemma</span> <a name="comp_actE"><span class="id" title="lemma">comp_actE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">e</span> : <a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e"><span class="id" title="variable">e</span></a>). <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afix_comp"><span class="id" title="lemma">afix_comp</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_comp_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afix_comp"><span class="id" title="lemma">afix_comp</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_comp_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#8e105dc0a5aeb045cc40eeab18015826"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_comp"><span class="id" title="lemma">astab_comp</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#619a2190d60a66179f3396458e2a09ae"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_comp"><span class="id" title="lemma">astab_comp</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#320f70d30c9a649ec82642b364681418"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_comp"><span class="id" title="lemma">astabs_comp</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#619a2190d60a66179f3396458e2a09ae"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_comp"><span class="id" title="lemma">astabs_comp</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#320f70d30c9a649ec82642b364681418"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#CompAct.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#CompAct"><span class="id" title="section">CompAct</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="835827ac44615432d269abaf103548c9"><span class="id" title="notation">"</span></a>to \o f" := (<a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a> <span class="id" title="var">to</span> <span class="id" title="var">f</span>) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="0ba45569cc72e3fb1011d7c0c5410446"><span class="id" title="notation">"</span></a>to \o f" := (<a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a> <span class="id" title="var">to</span> <span class="id" title="var">f</span>) : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="PermAction"><span class="id" title="section">PermAction</span></a>.<br/> @@ -1386,16 +1378,16 @@ <span class="id" title="keyword">Canonical</span> <span class="id" title="var">perm_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#Action"><span class="id" title="constructor">Action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aperm_is_action"><span class="id" title="lemma">aperm_is_action</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pcycleE"><span class="id" title="lemma">pcycleE</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.perm.html#pcycle"><span class="id" title="definition">pcycle</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation">]></span></a>%<span class="id" title="var">g</span>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pcycleE"><span class="id" title="lemma">pcycleE</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.perm.html#pcycle"><span class="id" title="definition">pcycle</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation">]></span></a>%<span class="id" title="var">g</span>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="perm_act1P"><span class="id" title="lemma">perm_act1P</span></a> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.perm.html#aperm"><span class="id" title="definition">aperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 1).<br/> +<span class="id" title="keyword">Lemma</span> <a name="perm_act1P"><span class="id" title="lemma">perm_act1P</span></a> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.perm.html#aperm"><span class="id" title="definition">aperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="perm_faithful"><span class="id" title="lemma">perm_faithful</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="perm_faithful"><span class="id" title="lemma">perm_faithful</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actperm_id"><span class="id" title="lemma">actperm_id</span></a> <span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actperm_id"><span class="id" title="lemma">actperm_id</span></a> <span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#PermAction"><span class="id" title="section">PermAction</span></a>.<br/> @@ -1403,22 +1395,22 @@ <br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">"</span></a>'P" := (<a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">"</span></a>'P" := (<a class="idref" href="mathcomp.fingroup.action.html#perm_action"><span class="id" title="definition">perm_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="ActpermOrbits"><span class="id" title="section">ActpermOrbits</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="ActpermOrbits.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActpermOrbits.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="ActpermOrbits.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="ActpermOrbits.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ActpermOrbits.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="ActpermOrbits.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> <span class="id" title="keyword">Variable</span> <a name="ActpermOrbits.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.rT"><span class="id" title="variable">rT</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbit_morphim_actperm"><span class="id" title="lemma">orbit_morphim_actperm</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbit_morphim_actperm"><span class="id" title="lemma">orbit_morphim_actperm</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="pcycle_actperm"><span class="id" title="lemma">pcycle_actperm</span></a> (<span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.aT"><span class="id" title="variable">aT</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.perm.html#pcycle"><span class="id" title="definition">pcycle</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation">]></span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.perm.html#pcycle"><span class="id" title="definition">pcycle</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation">]></span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#ActpermOrbits"><span class="id" title="section">ActpermOrbits</span></a>.<br/> @@ -1427,26 +1419,26 @@ <span class="id" title="keyword">Section</span> <a name="RestrictPerm"><span class="id" title="section">RestrictPerm</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RestrictPerm.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="RestrictPerm.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RestrictPerm.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="RestrictPerm.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="restr_perm"><span class="id" title="definition">restr_perm</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#subxx"><span class="id" title="lemma">subxx</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation">]></span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">restr_perm_morphism</span> := <a class="idref" href="mathcomp.fingroup.morphism.html#4638420a8c497f6fdfbc01376756a30a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#4638420a8c497f6fdfbc01376756a30a"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#4638420a8c497f6fdfbc01376756a30a"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#4638420a8c497f6fdfbc01376756a30a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="restr_perm"><span class="id" title="definition">restr_perm</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#subxx"><span class="id" title="lemma">subxx</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation">]></span></a>).<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">restr_perm_morphism</span> := <a class="idref" href="mathcomp.fingroup.morphism.html#d22b43813ec744a6a8786f15c9267991"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#d22b43813ec744a6a8786f15c9267991"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#d22b43813ec744a6a8786f15c9267991"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#d22b43813ec744a6a8786f15c9267991"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="restr_perm_on"><span class="id" title="lemma">restr_perm_on</span></a> <span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.perm.html#perm_on"><span class="id" title="definition">perm_on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="triv_restr_perm"><span class="id" title="lemma">triv_restr_perm</span></a> <span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1.<br/> +<span class="id" title="keyword">Lemma</span> <a name="triv_restr_perm"><span class="id" title="lemma">triv_restr_perm</span></a> <span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="restr_permE"><span class="id" title="lemma">restr_permE</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="restr_permE"><span class="id" title="lemma">restr_permE</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="ker_restr_perm"><span class="id" title="lemma">ker_restr_perm</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#034cc0eb573e9a86d9574eaed7b27a13"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#034cc0eb573e9a86d9574eaed7b27a13"><span class="id" title="notation">ker</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="ker_restr_perm"><span class="id" title="lemma">ker_restr_perm</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#7ef99623452370540bbc44fd30b0bc94"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#7ef99623452370540bbc44fd30b0bc94"><span class="id" title="notation">ker</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="im_restr_perm"><span class="id" title="lemma">im_restr_perm</span></a> <span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="im_restr_perm"><span class="id" title="lemma">im_restr_perm</span></a> <span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm.S"><span class="id" title="variable">S</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#RestrictPerm"><span class="id" title="section">RestrictPerm</span></a>.<br/> @@ -1458,27 +1450,27 @@ <span class="id" title="keyword">Variable</span> <a name="AutIn.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="Aut_in"><span class="id" title="definition">Aut_in</span></a> <span class="id" title="var">A</span> (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) := <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#d17cdb562dee90224eb90588920818d9"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Aut_in"><span class="id" title="definition">Aut_in</span></a> <span class="id" title="var">A</span> (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) := <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#29c15a80eba1871cc5ec8662b9f0468b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> <a name="AutIn.G"><span class="id" title="variable">G</span></a> <a name="AutIn.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="AutIn.sHG"><span class="id" title="variable">sHG</span></a>: <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Variables</span> <a name="AutIn.G"><span class="id" title="variable">G</span></a> <a name="AutIn.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Hypothesis</span> <a name="AutIn.sHG"><span class="id" title="variable">sHG</span></a>: <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Aut_restr_perm"><span class="id" title="lemma">Aut_restr_perm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Aut_restr_perm"><span class="id" title="lemma">Aut_restr_perm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="restr_perm_Aut"><span class="id" title="lemma">restr_perm_Aut</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="restr_perm_Aut"><span class="id" title="lemma">restr_perm_Aut</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Aut_in_isog"><span class="id" title="lemma">Aut_in_isog</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Aut_in_isog"><span class="id" title="lemma">Aut_in_isog</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.action.html#restr_perm"><span class="id" title="definition">restr_perm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="Aut_sub_fullP"><span class="id" title="lemma">Aut_sub_fullP</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">h</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>, <a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">g</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#g"><span class="id" title="variable">g</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#h"><span class="id" title="variable">h</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">]</span></a>)<br/> - (<a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a>).<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">h</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>, <a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">g</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#g"><span class="id" title="variable">g</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#h"><span class="id" title="variable">h</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">]</span></a>)<br/> + (<a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutIn.H"><span class="id" title="variable">H</span></a>).<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#AutIn"><span class="id" title="section">AutIn</span></a>.<br/> @@ -1489,27 +1481,27 @@ <span class="id" title="keyword">Section</span> <a name="InjmAutIn"><span class="id" title="section">InjmAutIn</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="InjmAutIn.gT"><span class="id" title="variable">gT</span></a> <a name="InjmAutIn.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="InjmAutIn.D"><span class="id" title="variable">D</span></a> <a name="InjmAutIn.G"><span class="id" title="variable">G</span></a> <a name="InjmAutIn.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="InjmAutIn.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="InjmAutIn.injf"><span class="id" title="variable">injf</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a>) (<a name="InjmAutIn.sGD"><span class="id" title="variable">sGD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.D"><span class="id" title="variable">D</span></a>) (<a name="InjmAutIn.sHG"><span class="id" title="variable">sHG</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="InjmAutIn.gT"><span class="id" title="variable">gT</span></a> <a name="InjmAutIn.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="InjmAutIn.D"><span class="id" title="variable">D</span></a> <a name="InjmAutIn.G"><span class="id" title="variable">G</span></a> <a name="InjmAutIn.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="InjmAutIn.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="InjmAutIn.injf"><span class="id" title="variable">injf</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a>) (<a name="InjmAutIn.sGD"><span class="id" title="variable">sGD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.D"><span class="id" title="variable">D</span></a>) (<a name="InjmAutIn.sHG"><span class="id" title="variable">sHG</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>).<br/> <span class="id" title="keyword">Let</span> <a name="InjmAutIn.sHD"><span class="id" title="variable">sHD</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#subset_trans"><span class="id" title="lemma">subset_trans</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.sHG"><span class="id" title="variable">sHG</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.sGD"><span class="id" title="variable">sGD</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="astabs_Aut_isom"><span class="id" title="lemma">astabs_Aut_isom</span></a> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#fGisom"><span class="id" title="abbreviation">fGisom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#fGisom"><span class="id" title="abbreviation">fGisom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="isom_restr_perm"><span class="id" title="lemma">isom_restr_perm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#fHisom"><span class="id" title="abbreviation">fHisom</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#inH"><span class="id" title="abbreviation">inH</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#infH"><span class="id" title="abbreviation">infH</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#fGisom"><span class="id" title="abbreviation">fGisom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="isom_restr_perm"><span class="id" title="lemma">isom_restr_perm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#fHisom"><span class="id" title="abbreviation">fHisom</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#inH"><span class="id" title="abbreviation">inH</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#infH"><span class="id" title="abbreviation">infH</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#fGisom"><span class="id" title="abbreviation">fGisom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="restr_perm_isom"><span class="id" title="lemma">restr_perm_isom</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#inH"><span class="id" title="abbreviation">inH</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#infH"><span class="id" title="abbreviation">infH</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>)) <a class="idref" href="mathcomp.fingroup.action.html#fHisom"><span class="id" title="abbreviation">fHisom</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="restr_perm_isom"><span class="id" title="lemma">restr_perm_isom</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#inH"><span class="id" title="abbreviation">inH</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#infH"><span class="id" title="abbreviation">infH</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>)) <a class="idref" href="mathcomp.fingroup.action.html#fHisom"><span class="id" title="abbreviation">fHisom</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="injm_Aut_sub"><span class="id" title="lemma">injm_Aut_sub</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>)) (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="injm_Aut_sub"><span class="id" title="lemma">injm_Aut_sub</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>)) (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="injm_Aut_full"><span class="id" title="lemma">injm_Aut_full</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>)) (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>)) (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Aut_in"><span class="id" title="definition">Aut_in</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn.H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#InjmAutIn"><span class="id" title="section">InjmAutIn</span></a>.<br/> @@ -1518,19 +1510,19 @@ <span class="id" title="keyword">Section</span> <a name="GroupAction"><span class="id" title="section">GroupAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="GroupAction.aT"><span class="id" title="variable">aT</span></a> <a name="GroupAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="GroupAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="GroupAction.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="GroupAction.aT"><span class="id" title="variable">aT</span></a> <a name="GroupAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="GroupAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="GroupAction.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="is_groupAction"><span class="id" title="definition">is_groupAction</span></a> (<span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#actT"><span class="id" title="abbreviation">actT</span></a>) :=<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupAction.R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupAction.R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Structure</span> <a name="groupAction"><span class="id" title="record">groupAction</span></a> := <a name="GroupAction"><span class="id" title="constructor">GroupAction</span></a> {<a name="gact"><span class="id" title="projection">gact</span></a> :> <a class="idref" href="mathcomp.fingroup.action.html#actT"><span class="id" title="abbreviation">actT</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gact"><span class="id" title="method">gact</span></a>}.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="clone_groupAction"><span class="id" title="definition">clone_groupAction</span></a> <span class="id" title="var">to</span> :=<br/> - <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <span class="id" title="var">_</span> <span class="id" title="var">toA</span> := <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">type</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">for</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#d7f4c4dc11bb6b98f0e78c197b6ba346"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <span class="id" title="var">_</span> <span class="id" title="tactic">in</span><br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">k</span> ⇒ <a class="idref" href="mathcomp.fingroup.action.html#k"><span class="id" title="variable">k</span></a> <span class="id" title="var">toA</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a>.<br/> + <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <span class="id" title="var">_</span> <span class="id" title="var">toA</span> := <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">type</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">for</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#daf095f6f58ec61a0b83a3c10c4f8017"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="var">_</span> <span class="id" title="tactic">in</span><br/> + <span class="id" title="keyword">fun</span> <span class="id" title="var">k</span> ⇒ <a class="idref" href="mathcomp.fingroup.action.html#k"><span class="id" title="variable">k</span></a> <span class="id" title="var">toA</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="section">GroupAction</span></a>.<br/> @@ -1541,7 +1533,7 @@ <br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="9c48f0d46104b2a59cfe6fb489695b9b"><span class="id" title="notation">"</span></a>[ 'groupAction' 'of' to ]" :=<br/> +<span class="id" title="keyword">Notation</span> <a name="1978e96f09b066b72f465983699c48ee"><span class="id" title="notation">"</span></a>[ 'groupAction' 'of' to ]" :=<br/> (<a class="idref" href="mathcomp.fingroup.action.html#clone_groupAction"><span class="id" title="definition">clone_groupAction</span></a> (@<a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">to</span>))<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'groupAction' 'of' to ]") : <span class="id" title="var">form_scope</span>.<br/> @@ -1549,27 +1541,27 @@ <span class="id" title="keyword">Section</span> <a name="GroupActionDefs"><span class="id" title="section">GroupActionDefs</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="GroupActionDefs.aT"><span class="id" title="variable">aT</span></a> <a name="GroupActionDefs.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="GroupActionDefs.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="GroupActionDefs.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="GroupActionDefs.aT"><span class="id" title="variable">aT</span></a> <a name="GroupActionDefs.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="GroupActionDefs.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="GroupActionDefs.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.R"><span class="id" title="variable">R</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="gact_range"><span class="id" title="definition">gact_range</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.R"><span class="id" title="variable">R</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.R"><span class="id" title="variable">R</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="gacent"><span class="id" title="definition">gacent</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> := <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="gacent"><span class="id" title="definition">gacent</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span> := <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="acts_on_group"><span class="id" title="definition">acts_on_group</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.R"><span class="id" title="variable">R</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="acts_on_group"><span class="id" title="definition">acts_on_group</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> := <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs.R"><span class="id" title="variable">R</span></a>.<br/> <br/> -<span class="id" title="keyword">Coercion</span> <span class="id" title="var">actby_cond_group</span> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#acts_on_group"><span class="id" title="definition">acts_on_group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actby_cond"><span class="id" title="definition">actby_cond</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> :=<br/> - @<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#proj1"><span class="id" title="lemma">proj1</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>.<br/> +<span class="id" title="keyword">Coercion</span> <span class="id" title="var">actby_cond_group</span> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#acts_on_group"><span class="id" title="definition">acts_on_group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actby_cond"><span class="id" title="definition">actby_cond</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a> :=<br/> + @<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#proj1"><span class="id" title="lemma">proj1</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> <span class="id" title="var">to</span> :=<br/> - <a class="idref" href="mathcomp.fingroup.fingroup.html#ff34d14fa7e7764d47d58a9547aa60ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ff34d14fa7e7764d47d58a9547aa60ae"><span class="id" title="notation">min</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ff34d14fa7e7764d47d58a9547aa60ae"><span class="id" title="notation">of</span></a> <span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#ff34d14fa7e7764d47d58a9547aa60ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#36625695d37b6869c156bfcdf13834f7"><span class="id" title="notation">:!=:</span></a> 1 <a class="idref" href="mathcomp.fingroup.fingroup.html#ff34d14fa7e7764d47d58a9547aa60ae"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ff34d14fa7e7764d47d58a9547aa60ae"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.fingroup.html#83949b4ab4a5556fc861a975723584d5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#83949b4ab4a5556fc861a975723584d5"><span class="id" title="notation">min</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#83949b4ab4a5556fc861a975723584d5"><span class="id" title="notation">of</span></a> <span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#83949b4ab4a5556fc861a975723584d5"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#be2f022a539ec6d4d51932b5ea998e57"><span class="id" title="notation">:!=:</span></a> 1 <a class="idref" href="mathcomp.fingroup.fingroup.html#83949b4ab4a5556fc861a975723584d5"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#83949b4ab4a5556fc861a975723584d5"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionDefs"><span class="id" title="section">GroupActionDefs</span></a>.<br/> @@ -1577,77 +1569,77 @@ <br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">"</span></a>''C_' ( | to ) ( A )" := (<a class="idref" href="mathcomp.fingroup.action.html#gacent"><span class="id" title="definition">gacent</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">"</span></a>''C_' ( | to ) ( A )" := (<a class="idref" href="mathcomp.fingroup.action.html#gacent"><span class="id" title="definition">gacent</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''C_' ( | to ) ( A )") : <span class="id" title="var">group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">"</span></a>''C_' ( G | to ) ( A )" := (<span class="id" title="var">G</span> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>)<br/> +<span class="id" title="keyword">Notation</span> <a name="2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">"</span></a>''C_' ( G | to ) ( A )" := (<span class="id" title="var">G</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''C_' ( G | to ) ( A )") : <span class="id" title="var">group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">"</span></a>''C_' ( | to ) [ a ]" := <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a><br/> +<span class="id" title="keyword">Notation</span> <a name="d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">"</span></a>''C_' ( | to ) [ a ]" := <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a><br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''C_' ( | to ) [ a ]") : <span class="id" title="var">group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="f003dba8fcf02dcc50c37ba6ada8b94d"><span class="id" title="notation">"</span></a>''C_' ( G | to ) [ a ]" := <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">(</span></a><span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)</span></a><br/> +<span class="id" title="keyword">Notation</span> <a name="09b4f258e8f241962aae3f52f18cfc9b"><span class="id" title="notation">"</span></a>''C_' ( G | to ) [ a ]" := <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">(</span></a><span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">|</span></a> <span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)</span></a><br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''C_' ( G | to ) [ a ]") : <span class="id" title="var">group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">"</span></a>{ 'acts' A , 'on' 'group' G | to }" := (<a class="idref" href="mathcomp.fingroup.action.html#acts_on_group"><span class="id" title="definition">acts_on_group</span></a> <span class="id" title="var">A</span> <span class="id" title="var">G</span> <span class="id" title="var">to</span>)<br/> +<span class="id" title="keyword">Notation</span> <a name="e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">"</span></a>{ 'acts' A , 'on' 'group' G | to }" := (<a class="idref" href="mathcomp.fingroup.action.html#acts_on_group"><span class="id" title="definition">acts_on_group</span></a> <span class="id" title="var">A</span> <span class="id" title="var">G</span> <span class="id" title="var">to</span>)<br/> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "{ 'acts' A , 'on' 'group' G | to }") : <span class="id" title="var">form_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="RawGroupAction"><span class="id" title="section">RawGroupAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RawGroupAction.aT"><span class="id" title="variable">aT</span></a> <a name="RawGroupAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="RawGroupAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="RawGroupAction.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RawGroupAction.aT"><span class="id" title="variable">aT</span></a> <a name="RawGroupAction.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="RawGroupAction.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="RawGroupAction.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <span class="id" title="keyword">Variable</span> <a name="RawGroupAction.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="actperm_Aut"><span class="id" title="lemma">actperm_Aut</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="im_actperm_Aut"><span class="id" title="lemma">im_actperm_Aut</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="im_actperm_Aut"><span class="id" title="lemma">im_actperm_Aut</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gact_out"><span class="id" title="lemma">gact_out</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gact_out"><span class="id" title="lemma">gact_out</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gactM"><span class="id" title="lemma">gactM</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gactM"><span class="id" title="lemma">gactM</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actmM"><span class="id" title="lemma">actmM</span></a> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actmM"><span class="id" title="lemma">actmM</span></a> <span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">act_morphism</span> <span class="id" title="var">a</span> := <a class="idref" href="mathcomp.fingroup.morphism.html#Morphism"><span class="id" title="constructor">Morphism</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#actmM"><span class="id" title="lemma">actmM</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="morphim_actm"><span class="id" title="lemma">morphim_actm</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>), <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#54d9268ab0ed9ca3b605c1679d80e7b8"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>), <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71ba62ddcc2adca90a3552e0f4042726"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="RawGroupAction.a"><span class="id" title="variable">a</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.aT"><span class="id" title="variable">aT</span></a>) (<a name="RawGroupAction.A"><span class="id" title="variable">A</span></a> <a name="RawGroupAction.B"><span class="id" title="variable">B</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="RawGroupAction.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RawGroupAction.a"><span class="id" title="variable">a</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.aT"><span class="id" title="variable">aT</span></a>) (<a name="RawGroupAction.A"><span class="id" title="variable">A</span></a> <a name="RawGroupAction.B"><span class="id" title="variable">B</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="RawGroupAction.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentIdom"><span class="id" title="lemma">gacentIdom</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentIdom"><span class="id" title="lemma">gacentIdom</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentIim"><span class="id" title="lemma">gacentIim</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentIim"><span class="id" title="lemma">gacentIim</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentS"><span class="id" title="lemma">gacentS</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentS"><span class="id" title="lemma">gacentS</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentU"><span class="id" title="lemma">gacentU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#52f608a788da136ac97df132d7055463"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentU"><span class="id" title="lemma">gacentU</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="RawGroupAction.Da"><span class="id" title="variable">Da</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a>) (<a name="RawGroupAction.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a>) (<a name="RawGroupAction.sSR"><span class="id" title="variable">sSR</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a>).<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="RawGroupAction.Da"><span class="id" title="variable">Da</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a>) (<a name="RawGroupAction.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.D"><span class="id" title="variable">D</span></a>) (<a name="RawGroupAction.sSR"><span class="id" title="variable">sSR</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentE"><span class="id" title="lemma">gacentE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentE"><span class="id" title="lemma">gacentE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacent1E"><span class="id" title="lemma">gacent1E</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacent1E"><span class="id" title="lemma">gacent1E</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="subgacentE"><span class="id" title="lemma">subgacentE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="subgacentE"><span class="id" title="lemma">subgacentE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="subgacent1E"><span class="id" title="lemma">subgacent1E</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#f003dba8fcf02dcc50c37ba6ada8b94d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f003dba8fcf02dcc50c37ba6ada8b94d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#f003dba8fcf02dcc50c37ba6ada8b94d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f003dba8fcf02dcc50c37ba6ada8b94d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f003dba8fcf02dcc50c37ba6ada8b94d"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#f003dba8fcf02dcc50c37ba6ada8b94d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#d332864708f1d0e9a3a13805c0663964"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="subgacent1E"><span class="id" title="lemma">subgacent1E</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#09b4f258e8f241962aae3f52f18cfc9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#09b4f258e8f241962aae3f52f18cfc9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#09b4f258e8f241962aae3f52f18cfc9b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#09b4f258e8f241962aae3f52f18cfc9b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#09b4f258e8f241962aae3f52f18cfc9b"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#09b4f258e8f241962aae3f52f18cfc9b"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction.a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#2bb94d3d01f9b00932888c009233b945"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#RawGroupAction"><span class="id" title="section">RawGroupAction</span></a>.<br/> @@ -1657,130 +1649,130 @@ <br/> <span class="id" title="keyword">Variables</span> <a name="GroupActionTheory.aT"><span class="id" title="variable">aT</span></a> <a name="GroupActionTheory.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#R"><span class="id" title="variable">R</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">M</span> <span class="id" title="var">N</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.to"><span class="id" title="variable">to</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.action.html#R"><span class="id" title="variable">R</span></a>).<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">M</span> <span class="id" title="var">N</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gact1"><span class="id" title="lemma">gact1</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> 1 <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gact1"><span class="id" title="lemma">gact1</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> 1 <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gactV"><span class="id" title="lemma">gactV</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gactV"><span class="id" title="lemma">gactV</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gactX"><span class="id" title="lemma">gactX</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">n</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#86a04fb564fb97d388cad84a3a204260"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.fingroup.action.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c3c88e2b30b681cd767a54649faf5973"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gactX"><span class="id" title="lemma">gactX</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">n</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#06cdd2633d7788bac7abeac13b2dd91e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.fingroup.action.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#3d6621e6eef40dcc7dc9a612222d0b4e"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gactJ"><span class="id" title="lemma">gactJ</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#808c6b8e35e792f23899f360a21e4638"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gactJ"><span class="id" title="lemma">gactJ</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gactR"><span class="id" title="lemma">gactR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#d5d566f861753940ef0e9a18d348c2b8"><span class="id" title="notation">[~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d5d566f861753940ef0e9a18d348c2b8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d5d566f861753940ef0e9a18d348c2b8"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3014e73af2a90fd800d8681479d76336"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gactR"><span class="id" title="lemma">gactR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#fd6a490bd0f786b0eb5a7c1f70a1610e"><span class="id" title="notation">[~</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#fd6a490bd0f786b0eb5a7c1f70a1610e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#fd6a490bd0f786b0eb5a7c1f70a1610e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gact_stable"><span class="id" title="lemma">gact_stable</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gact_stable"><span class="id" title="lemma">gact_stable</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="group_set_gacent"><span class="id" title="lemma">group_set_gacent</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_gacent"><span class="id" title="lemma">group_set_gacent</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">gacent_group</span> <span class="id" title="var">A</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#group_set_gacent"><span class="id" title="lemma">group_set_gacent</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacent1"><span class="id" title="lemma">gacent1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacent1"><span class="id" title="lemma">gacent1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacent_gen"><span class="id" title="lemma">gacent_gen</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation">>></span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacent_gen"><span class="id" title="lemma">gacent_gen</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">>></span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentD1"><span class="id" title="lemma">gacentD1</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentD1"><span class="id" title="lemma">gacentD1</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacent_cycle"><span class="id" title="lemma">gacent_cycle</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#30152704c0ab4066186d0284456667e8"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#61d1bba23e27ff161a7de70cf7f24d12"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacent_cycle"><span class="id" title="lemma">gacent_cycle</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#5e5825d099c952c2db2842c142cbde94"><span class="id" title="notation">]></span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.action.html#d9bffdd101b88473ac9226b8ece080fc"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="gacentY"><span class="id" title="lemma">gacentY</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#80208730563aa86aa7861f6fe1b846da"><span class="id" title="notation"><*></span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0d7ccd69af81527d9facc6293603bbef"><span class="id" title="notation"><*></span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="gacentM"><span class="id" title="lemma">gacentM</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1"><span class="id" title="lemma">astab1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a>1 <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1"><span class="id" title="lemma">astab1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a>1 <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_range"><span class="id" title="lemma">astab_range</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_range"><span class="id" title="lemma">astab_range</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="gacentC"><span class="id" title="lemma">gacentC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab_gen"><span class="id" title="lemma">astab_gen</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation">>></span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab_gen"><span class="id" title="lemma">astab_gen</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">>></span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="astabM"><span class="id" title="lemma">astabM</span></a> <span class="id" title="var">M</span> <span class="id" title="var">N</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs1"><span class="id" title="lemma">astabs1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a>1 <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs1"><span class="id" title="lemma">astabs1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a>1 <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabs_range"><span class="id" title="lemma">astabs_range</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabs_range"><span class="id" title="lemma">astabs_range</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsD1"><span class="id" title="lemma">astabsD1</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsD1"><span class="id" title="lemma">astabsD1</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacts_range"><span class="id" title="lemma">gacts_range</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacts_range"><span class="id" title="lemma">gacts_range</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_subnorm_gacent"><span class="id" title="lemma">acts_subnorm_gacent</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_subnorm_gacent"><span class="id" title="lemma">acts_subnorm_gacent</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_subnorm_subgacent"><span class="id" title="lemma">acts_subnorm_subgacent</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_gen"><span class="id" title="lemma">acts_gen</span></a> <span class="id" title="var">A</span> <span class="id" title="var">S</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation">>></span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">>></span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_joing"><span class="id" title="lemma">acts_joing</span></a> <span class="id" title="var">A</span> <span class="id" title="var">M</span> <span class="id" title="var">N</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#80208730563aa86aa7861f6fe1b846da"><span class="id" title="notation"><*></span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0d7ccd69af81527d9facc6293603bbef"><span class="id" title="notation"><*></span></a> <a class="idref" href="mathcomp.fingroup.action.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="injm_actm"><span class="id" title="lemma">injm_actm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#14bfb149f00fa839cfb11397f4fe629f"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="injm_actm"><span class="id" title="lemma">injm_actm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">injm</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#3a01b501aff42699ca141d6279e9102f"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="im_actm"><span class="id" title="lemma">im_actm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="im_actm"><span class="id" title="lemma">im_actm</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#actm"><span class="id" title="definition">actm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_char"><span class="id" title="lemma">acts_char</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#004858100bfba9714bde1cdbce60358b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.automorphism.html#004858100bfba9714bde1cdbce60358b"><span class="id" title="notation">char</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_char"><span class="id" title="lemma">acts_char</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#d9dc63f0c53bc5e6f232c50d48c40709"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.automorphism.html#d9dc63f0c53bc5e6f232c50d48c40709"><span class="id" title="notation">char</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="gacts_char"><span class="id" title="lemma">gacts_char</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#004858100bfba9714bde1cdbce60358b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.automorphism.html#004858100bfba9714bde1cdbce60358b"><span class="id" title="notation">char</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">}</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.automorphism.html#d9dc63f0c53bc5e6f232c50d48c40709"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.automorphism.html#d9dc63f0c53bc5e6f232c50d48c40709"><span class="id" title="notation">char</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="GroupActionTheory.Restrict"><span class="id" title="section">Restrict</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.Restrict.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.Restrict.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.Restrict.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.Restrict.sAD"><span class="id" title="variable">sAD</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="ract_is_groupAction"><span class="id" title="lemma">ract_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Restrict.sAD"><span class="id" title="variable">sAD</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="ract_is_groupAction"><span class="id" title="lemma">ract_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Restrict.sAD"><span class="id" title="variable">sAD</span></a>).<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">ract_groupAction</span> := <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ract_is_groupAction"><span class="id" title="lemma">ract_is_groupAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacent_ract"><span class="id" title="lemma">gacent_ract</span></a> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#ract_groupAction"><span class="id" title="definition">ract_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Restrict.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacent_ract"><span class="id" title="lemma">gacent_ract</span></a> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#ract_groupAction"><span class="id" title="definition">ract_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Restrict.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Restrict"><span class="id" title="section">Restrict</span></a>.<br/> @@ -1789,17 +1781,17 @@ <span class="id" title="keyword">Section</span> <a name="GroupActionTheory.ActBy"><span class="id" title="section">ActBy</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.ActBy.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.ActBy.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.ActBy.nGAg"><span class="id" title="variable">nGAg</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#942d78c074baecb495cbc019394dd5b3"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.ActBy.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.ActBy.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.ActBy.nGAg"><span class="id" title="variable">nGAg</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e0999a2c5d268a8ec2a8f8a47338efa4"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actby_is_groupAction"><span class="id" title="lemma">actby_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.nGAg"><span class="id" title="variable">nGAg</span></a><a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation">]></span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actby_is_groupAction"><span class="id" title="lemma">actby_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.nGAg"><span class="id" title="variable">nGAg</span></a><a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation">]></span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">actby_groupAction</span> := <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#actby_is_groupAction"><span class="id" title="lemma">actby_is_groupAction</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="gacent_actby"><span class="id" title="lemma">gacent_actby</span></a> <span class="id" title="var">B</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#actby_groupAction"><span class="id" title="definition">actby_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#actby_groupAction"><span class="id" title="definition">actby_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.ActBy"><span class="id" title="section">ActBy</span></a>.<br/> @@ -1808,19 +1800,19 @@ <span class="id" title="keyword">Section</span> <a name="GroupActionTheory.Quotient"><span class="id" title="section">Quotient</span></a>.<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="acts_qact_dom_norm"><span class="id" title="lemma">acts_qact_dom_norm</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="acts_qact_dom_norm"><span class="id" title="lemma">acts_qact_dom_norm</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="qact_is_groupAction"><span class="id" title="lemma">qact_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2e4ccc4d97341df4136dd243a5fe1a5c"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="qact_is_groupAction"><span class="id" title="lemma">qact_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad04e00ef26e546e5433da83c9f70dee"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a>).<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">quotient_groupAction</span> := <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_is_groupAction"><span class="id" title="lemma">qact_is_groupAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="qact_domE"><span class="id" title="lemma">qact_domE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="qact_domE"><span class="id" title="lemma">qact_domE</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Quotient"><span class="id" title="section">Quotient</span></a>.<br/> @@ -1829,52 +1821,52 @@ <span class="id" title="keyword">Section</span> <a name="GroupActionTheory.Mod"><span class="id" title="section">Mod</span></a>.<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="modact_is_groupAction"><span class="id" title="lemma">modact_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2763ae1d41d6f4b536ed07b20d50de88"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="modact_is_groupAction"><span class="id" title="lemma">modact_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a31739c14704f62c7a05474f0d8f2ec1"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a>).<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">mod_groupAction</span> := <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#modact_is_groupAction"><span class="id" title="lemma">modact_is_groupAction</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="modgactE"><span class="id" title="lemma">modgactE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2763ae1d41d6f4b536ed07b20d50de88"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a>)%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_D</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a31739c14704f62c7a05474f0d8f2ec1"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a>)%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="gacent_mod"><span class="id" title="lemma">gacent_mod</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#80a58c159fbe61cbb7996107e4e1da9b"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#2ae6f5a80bf45b13993075049a02e31d"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_irr_mod"><span class="id" title="lemma">acts_irr_mod</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod.H"><span class="id" title="variable">H</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.Mod"><span class="id" title="section">Mod</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="modact_coset_astab"><span class="id" title="lemma">modact_coset_astab</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2763ae1d41d6f4b536ed07b20d50de88"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#241fd4471d2bcb8850364ee8be828b4a"><span class="id" title="notation">)</span></a>)%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a31739c14704f62c7a05474f0d8f2ec1"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#1712a67728d9e50a104f9fd8eaad1b66"><span class="id" title="notation">)</span></a>)%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="acts_irr_mod_astab"><span class="id" title="lemma">acts_irr_mod_astab</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#652d6cc67746e5361142d90686607781"><span class="id" title="notation">)</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a> <span class="id" title="var">_</span>).<br/> + <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#6998185c5f7a5efd284e9c25133c5e71"><span class="id" title="notation">)</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a> <span class="id" title="var">_</span>).<br/> <br/> <span class="id" title="keyword">Section</span> <a name="GroupActionTheory.CompAct"><span class="id" title="section">CompAct</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.CompAct.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="GroupActionTheory.CompAct.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.CompAct.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="GroupActionTheory.CompAct.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="GroupActionTheory.CompAct.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="GroupActionTheory.CompAct.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>).<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="comp_is_groupAction"><span class="id" title="lemma">comp_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.R"><span class="id" title="variable">R</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#comp_action"><span class="id" title="definition">comp_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.CompAct.f"><span class="id" title="variable">f</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">comp_groupAction</span> := <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#comp_is_groupAction"><span class="id" title="lemma">comp_is_groupAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacent_comp"><span class="id" title="lemma">gacent_comp</span></a> <span class="id" title="var">U</span> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#comp_groupAction"><span class="id" title="definition">comp_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#U"><span class="id" title="variable">U</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#U"><span class="id" title="variable">U</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacent_comp"><span class="id" title="lemma">gacent_comp</span></a> <span class="id" title="var">U</span> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#comp_groupAction"><span class="id" title="definition">comp_groupAction</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#U"><span class="id" title="variable">U</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.to"><span class="id" title="variable">to</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.CompAct.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#U"><span class="id" title="variable">U</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory.CompAct"><span class="id" title="section">CompAct</span></a>.<br/> @@ -1883,19 +1875,19 @@ <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#GroupActionTheory"><span class="id" title="section">GroupActionTheory</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="172d6d57d3711fc7c98e224a1ba08aa5"><span class="id" title="notation">"</span></a>''C_' ( | to ) ( A )" := (<a class="idref" href="mathcomp.fingroup.action.html#gacent_group"><span class="id" title="definition">gacent_group</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="21d18710edc732547be12d2aad92fc55"><span class="id" title="notation">"</span></a>''C_' ( G | to ) ( A )" :=<br/> - (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.action.html#172d6d57d3711fc7c98e224a1ba08aa5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#172d6d57d3711fc7c98e224a1ba08aa5"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#172d6d57d3711fc7c98e224a1ba08aa5"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#172d6d57d3711fc7c98e224a1ba08aa5"><span class="id" title="notation">)(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#172d6d57d3711fc7c98e224a1ba08aa5"><span class="id" title="notation">)</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="4356e7bfd850205078f909c5323b38d5"><span class="id" title="notation">"</span></a>''C_' ( | to ) [ a ]" := (<a class="idref" href="mathcomp.fingroup.action.html#gacent_group"><span class="id" title="definition">gacent_group</span></a> <span class="id" title="var">to</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span>%<span class="id" title="var">g</span><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="cd7ed9e932fd7248ad04885bdad6bf8e"><span class="id" title="notation">"</span></a>''C_' ( G | to ) [ a ]" :=<br/> - (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.action.html#4356e7bfd850205078f909c5323b38d5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#4356e7bfd850205078f909c5323b38d5"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#4356e7bfd850205078f909c5323b38d5"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#4356e7bfd850205078f909c5323b38d5"><span class="id" title="notation">)[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.fingroup.action.html#4356e7bfd850205078f909c5323b38d5"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="d335a5aad6d2283dbae9fafc3ac65925"><span class="id" title="notation">"</span></a>''C_' ( | to ) ( A )" := (<a class="idref" href="mathcomp.fingroup.action.html#gacent_group"><span class="id" title="definition">gacent_group</span></a> <span class="id" title="var">to</span> <span class="id" title="var">A</span>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="ad7e04697a41ef1cca22addd3c6c6fe7"><span class="id" title="notation">"</span></a>''C_' ( G | to ) ( A )" :=<br/> + (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.action.html#d335a5aad6d2283dbae9fafc3ac65925"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#d335a5aad6d2283dbae9fafc3ac65925"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#d335a5aad6d2283dbae9fafc3ac65925"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#d335a5aad6d2283dbae9fafc3ac65925"><span class="id" title="notation">)(</span></a><span class="id" title="var">A</span><a class="idref" href="mathcomp.fingroup.action.html#d335a5aad6d2283dbae9fafc3ac65925"><span class="id" title="notation">)</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="6bafa22ec380d75f78daa3a91d981dc3"><span class="id" title="notation">"</span></a>''C_' ( | to ) [ a ]" := (<a class="idref" href="mathcomp.fingroup.action.html#gacent_group"><span class="id" title="definition">gacent_group</span></a> <span class="id" title="var">to</span> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span>%<span class="id" title="var">g</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="f72c1dae9b9e15817b3b2001c43d1004"><span class="id" title="notation">"</span></a>''C_' ( G | to ) [ a ]" :=<br/> + (<a class="idref" href="mathcomp.fingroup.fingroup.html#setI_group"><span class="id" title="definition">setI_group</span></a> <span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.action.html#6bafa22ec380d75f78daa3a91d981dc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bafa22ec380d75f78daa3a91d981dc3"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bafa22ec380d75f78daa3a91d981dc3"><span class="id" title="notation">(|</span></a><span class="id" title="var">to</span><a class="idref" href="mathcomp.fingroup.action.html#6bafa22ec380d75f78daa3a91d981dc3"><span class="id" title="notation">)[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.fingroup.action.html#6bafa22ec380d75f78daa3a91d981dc3"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">Group_scope</span>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="9590c91d152ef8d2e38e09f16e80a814"><span class="id" title="notation">"</span></a>to \ sAD" := (<a class="idref" href="mathcomp.fingroup.action.html#ract_groupAction"><span class="id" title="definition">ract_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">sAD</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="6ecf966a3859b7d1751aa41c1213e466"><span class="id" title="notation">"</span></a><[ nGA ] >" := (<a class="idref" href="mathcomp.fingroup.action.html#actby_groupAction"><span class="id" title="definition">actby_groupAction</span></a> <span class="id" title="var">nGA</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="2756d213ba2c3f60f8b9fc530f7c4cdc"><span class="id" title="notation">"</span></a>to / H" := (<a class="idref" href="mathcomp.fingroup.action.html#quotient_groupAction"><span class="id" title="definition">quotient_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="1f68cf81bb7cfeedd6167d6fc0c539cc"><span class="id" title="notation">"</span></a>to %% H" := (<a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="66f424a4bc70f81c17ca6c6cb9254216"><span class="id" title="notation">"</span></a>to \o f" := (<a class="idref" href="mathcomp.fingroup.action.html#comp_groupAction"><span class="id" title="definition">comp_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">f</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="d7db4b400ec3a447b82b23baa20981c9"><span class="id" title="notation">"</span></a>to \ sAD" := (<a class="idref" href="mathcomp.fingroup.action.html#ract_groupAction"><span class="id" title="definition">ract_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">sAD</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="c6b62d71cf339c64ec088331b40c48ae"><span class="id" title="notation">"</span></a><[ nGA ] >" := (<a class="idref" href="mathcomp.fingroup.action.html#actby_groupAction"><span class="id" title="definition">actby_groupAction</span></a> <span class="id" title="var">nGA</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="41672295fce40becd46688b39618a9e3"><span class="id" title="notation">"</span></a>to / H" := (<a class="idref" href="mathcomp.fingroup.action.html#quotient_groupAction"><span class="id" title="definition">quotient_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="6b58373623c34ddadc2ae0ec9c213052"><span class="id" title="notation">"</span></a>to %% H" := (<a class="idref" href="mathcomp.fingroup.action.html#mod_groupAction"><span class="id" title="definition">mod_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">H</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="491da8710c1c30436279d34f447955d4"><span class="id" title="notation">"</span></a>to \o f" := (<a class="idref" href="mathcomp.fingroup.action.html#comp_groupAction"><span class="id" title="definition">comp_groupAction</span></a> <span class="id" title="var">to</span> <span class="id" title="var">f</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> <br/> </div> @@ -1908,23 +1900,23 @@ <br/> <span class="id" title="keyword">Variables</span> (<a name="MorphAction.aT1"><span class="id" title="variable">aT1</span></a> <a name="MorphAction.aT2"><span class="id" title="variable">aT2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="MorphAction.rT1"><span class="id" title="variable">rT1</span></a> <a name="MorphAction.rT2"><span class="id" title="variable">rT2</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="MorphAction.D1"><span class="id" title="variable">D1</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="MorphAction.D2"><span class="id" title="variable">D2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="MorphAction.D1"><span class="id" title="variable">D1</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="MorphAction.D2"><span class="id" title="variable">D2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> <span class="id" title="keyword">Variables</span> (<a name="MorphAction.to1"><span class="id" title="variable">to1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT1"><span class="id" title="variable">rT1</span></a>) (<a name="MorphAction.to2"><span class="id" title="variable">to2</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#action"><span class="id" title="record">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT2"><span class="id" title="variable">rT2</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="MorphAction.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<a name="MorphAction.R"><span class="id" title="variable">R</span></a> <a name="MorphAction.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="MorphAction.h"><span class="id" title="variable">h</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT1"><span class="id" title="variable">rT1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT2"><span class="id" title="variable">rT2</span></a>) (<a name="MorphAction.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="MorphAction.actsDR"><span class="id" title="variable">actsDR</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#05449e0e2f87f06fca16a62c49e8b809"><span class="id" title="notation">}</span></a>) (<a name="MorphAction.injh"><span class="id" title="variable">injh</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="MorphAction.defD2"><span class="id" title="variable">defD2</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D2"><span class="id" title="variable">D2</span></a>.<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="MorphAction.sSR"><span class="id" title="variable">sSR</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.R"><span class="id" title="variable">R</span></a>) (<a name="MorphAction.sAD1"><span class="id" title="variable">sAD1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a>).<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="MorphAction.hfJ"><span class="id" title="variable">hfJ</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_act"><span class="id" title="definition">morph_act</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="MorphAction.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="MorphAction.R"><span class="id" title="variable">R</span></a> <a name="MorphAction.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="MorphAction.h"><span class="id" title="variable">h</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT1"><span class="id" title="variable">rT1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.rT2"><span class="id" title="variable">rT2</span></a>) (<a name="MorphAction.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="MorphAction.actsDR"><span class="id" title="variable">actsDR</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#5f6ba238defaa44d6a01a22efc00d730"><span class="id" title="notation">}</span></a>) (<a name="MorphAction.injh"><span class="id" title="variable">injh</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Hypothesis</span> <a name="MorphAction.defD2"><span class="id" title="variable">defD2</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D2"><span class="id" title="variable">D2</span></a>.<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="MorphAction.sSR"><span class="id" title="variable">sSR</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.R"><span class="id" title="variable">R</span></a>) (<a name="MorphAction.sAD1"><span class="id" title="variable">sAD1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a>).<br/> +<span class="id" title="keyword">Hypothesis</span> <a name="MorphAction.hfJ"><span class="id" title="variable">hfJ</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_act"><span class="id" title="definition">morph_act</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="morph_astabs"><span class="id" title="lemma">morph_astabs</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="morph_astabs"><span class="id" title="lemma">morph_astabs</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="morph_astab"><span class="id" title="lemma">morph_astab</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="morph_astab"><span class="id" title="lemma">morph_astab</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="morph_afix"><span class="id" title="lemma">morph_afix</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="morph_afix"><span class="id" title="lemma">morph_afix</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#MorphAction"><span class="id" title="section">MorphAction</span></a>.<br/> @@ -1934,27 +1926,27 @@ <br/> <span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.aT1"><span class="id" title="variable">aT1</span></a> <a name="MorphGroupAction.aT2"><span class="id" title="variable">aT2</span></a> <a name="MorphGroupAction.rT1"><span class="id" title="variable">rT1</span></a> <a name="MorphGroupAction.rT2"><span class="id" title="variable">rT2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="MorphGroupAction.D2"><span class="id" title="variable">D2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="MorphGroupAction.R2"><span class="id" title="variable">R2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT2"><span class="id" title="variable">rT2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="MorphGroupAction.D2"><span class="id" title="variable">D2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="MorphGroupAction.R2"><span class="id" title="variable">R2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT2"><span class="id" title="variable">rT2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> <span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.to1"><span class="id" title="variable">to1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a>) (<a name="MorphGroupAction.to2"><span class="id" title="variable">to2</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#groupAction"><span class="id" title="record">groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R2"><span class="id" title="variable">R2</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.h"><span class="id" title="variable">h</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT2"><span class="id" title="variable">rT2</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>) (<a name="MorphGroupAction.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="MorphGroupAction.h"><span class="id" title="variable">h</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT2"><span class="id" title="variable">rT2</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>) (<a name="MorphGroupAction.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>).<br/> <span class="id" title="keyword">Hypotheses</span> (<a name="MorphGroupAction.iso_h"><span class="id" title="variable">iso_h</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a>) (<a name="MorphGroupAction.iso_f"><span class="id" title="variable">iso_f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a>).<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="MorphGroupAction.hfJ"><span class="id" title="variable">hfJ</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_act"><span class="id" title="definition">morph_act</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#208bc995000a6307bdbc043c43919d97"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">M</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Hypothesis</span> <a name="MorphGroupAction.hfJ"><span class="id" title="variable">hfJ</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#morph_act"><span class="id" title="definition">morph_act</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">M</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.rT1"><span class="id" title="variable">rT1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="morph_gastabs"><span class="id" title="lemma">morph_gastabs</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="morph_gastabs"><span class="id" title="lemma">morph_gastabs</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="morph_gastab"><span class="id" title="lemma">morph_gastab</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="morph_gastab"><span class="id" title="lemma">morph_gastab</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="morph_gacent"><span class="id" title="lemma">morph_gacent</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="morph_gacent"><span class="id" title="lemma">morph_gacent</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="morph_gact_irr"><span class="id" title="lemma">morph_gact_irr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">M</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <br/> - <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <br/> + <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to2"><span class="id" title="variable">to2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction.to1"><span class="id" title="variable">to1</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#MorphGroupAction"><span class="id" title="section">MorphGroupAction</span></a>.<br/> @@ -1970,8 +1962,8 @@ <br/> <span class="id" title="keyword">Variable</span> <a name="InternalActionDefs.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalActionDefs.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalActionDefs.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalActionDefs.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalActionDefs.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> <br/> </div> @@ -2012,22 +2004,22 @@ <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#InternalActionDefs"><span class="id" title="section">InternalActionDefs</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">"</span></a>'R" := (@<a class="idref" href="mathcomp.fingroup.action.html#mulgr_action"><span class="id" title="definition">mulgr_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">"</span></a>'Rs" := (@<a class="idref" href="mathcomp.fingroup.action.html#rcoset_action"><span class="id" title="definition">rcoset_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">"</span></a>'J" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjg_action"><span class="id" title="definition">conjg_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="4ff57707e8e91cdc242380a7a9082e82"><span class="id" title="notation">"</span></a>'J" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjg_groupAction"><span class="id" title="definition">conjg_groupAction</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">groupAction_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="f05bcd008f250563fa67537a776ea961"><span class="id" title="notation">"</span></a>'Js" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjsg_action"><span class="id" title="definition">conjsg_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="cdd023ccc2efe92dd3cc3bafec9e78af"><span class="id" title="notation">"</span></a>'JG" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjG_action"><span class="id" title="definition">conjG_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">"</span></a>'Q" := (<a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2e4ccc4d97341df4136dd243a5fe1a5c"><span class="id" title="notation">/</span></a> <span class="id" title="var">_</span>)%<span class="id" title="var">act</span> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a18f700a73b74a8543514202563c13c4"><span class="id" title="notation">"</span></a>'Q" := (<a class="idref" href="mathcomp.fingroup.action.html#4ff57707e8e91cdc242380a7a9082e82"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#4ff57707e8e91cdc242380a7a9082e82"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#2756d213ba2c3f60f8b9fc530f7c4cdc"><span class="id" title="notation">/</span></a> <span class="id" title="var">_</span>)%<span class="id" title="var">gact</span> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">"</span></a>'R" := (@<a class="idref" href="mathcomp.fingroup.action.html#mulgr_action"><span class="id" title="definition">mulgr_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">"</span></a>'Rs" := (@<a class="idref" href="mathcomp.fingroup.action.html#rcoset_action"><span class="id" title="definition">rcoset_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">"</span></a>'J" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjg_action"><span class="id" title="definition">conjg_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="a109fdcf21cc4aa5e2550ec2a3a49ee1"><span class="id" title="notation">"</span></a>'J" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjg_groupAction"><span class="id" title="definition">conjg_groupAction</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="22e8687cfe5bb55e5bdea729ad5c72c1"><span class="id" title="notation">"</span></a>'Js" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjsg_action"><span class="id" title="definition">conjsg_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="9cb8ec4e4ed9f2067382df1e9eea44f5"><span class="id" title="notation">"</span></a>'JG" := (@<a class="idref" href="mathcomp.fingroup.action.html#conjG_action"><span class="id" title="definition">conjG_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">"</span></a>'Q" := (<a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad04e00ef26e546e5433da83c9f70dee"><span class="id" title="notation">/</span></a> <span class="id" title="var">_</span>)%<span class="id" title="var">act</span> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="7dcafbe20414081f1fadfdd82eb4964c"><span class="id" title="notation">"</span></a>'Q" := (<a class="idref" href="mathcomp.fingroup.action.html#a109fdcf21cc4aa5e2550ec2a3a49ee1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#a109fdcf21cc4aa5e2550ec2a3a49ee1"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#41672295fce40becd46688b39618a9e3"><span class="id" title="notation">/</span></a> <span class="id" title="var">_</span>)%<span class="id" title="var">gact</span> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">groupAction_scope</span>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="InternalGroupAction"><span class="id" title="section">InternalGroupAction</span></a>.<br/> <br/> <span class="id" title="keyword">Variable</span> <a name="InternalGroupAction.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> <span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a>.<br/> <br/> @@ -2039,73 +2031,73 @@ <div class="code"> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbitR"><span class="id" title="lemma">orbitR</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7a1b86b3dd47c101ea1643c2a591eaf1"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="orbitR"><span class="id" title="lemma">orbitR</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#4df0d598fb6ea95308004f1a1fa2d9ff"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1R"><span class="id" title="lemma">astab1R</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1R"><span class="id" title="lemma">astab1R</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabR"><span class="id" title="lemma">astabR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabR"><span class="id" title="lemma">astabR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsR"><span class="id" title="lemma">astabsR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsR"><span class="id" title="lemma">astabsR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="atransR"><span class="id" title="lemma">atransR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="atransR"><span class="id" title="lemma">atransR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="faithfulR"><span class="id" title="lemma">faithfulR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#78176c90a6fd5acd7c52e3779488c085"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e1bf5287bfc6397badc2a71c227e8d0"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="faithfulR"><span class="id" title="lemma">faithfulR</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">faithful</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#264f90218c4e4d8d1adb894ea52017ff"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <span class="id" title="var">G</span> := <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#atrans_acts"><span class="id" title="lemma">atrans_acts</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#atransR"><span class="id" title="lemma">atransR</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>)<a class="idref" href="mathcomp.fingroup.action.html#43026b5788d0e3ac602219a41766cc2f"><span class="id" title="notation">]></span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <span class="id" title="var">G</span> := <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation"><[</span></a><a class="idref" href="mathcomp.fingroup.action.html#atrans_acts"><span class="id" title="lemma">atrans_acts</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#atransR"><span class="id" title="lemma">atransR</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>)<a class="idref" href="mathcomp.fingroup.action.html#646c0d69b8fdffbfb4e9198bb1ae7c21"><span class="id" title="notation">]></span></a>.<br/> <br/> -<span class="id" title="keyword">Theorem</span> <a name="Cayley_isom"><span class="id" title="lemma">Cayley_isom</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>).<br/> +<span class="id" title="keyword">Theorem</span> <a name="Cayley_isom"><span class="id" title="lemma">Cayley_isom</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>) (<a class="idref" href="mathcomp.fingroup.action.html#Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>).<br/> <br/> -<span class="id" title="keyword">Theorem</span> <a name="Cayley_isog"><span class="id" title="lemma">Cayley_isog</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#cec6c3028572f2d4d267ecf02dc64058"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Theorem</span> <a name="Cayley_isog"><span class="id" title="lemma">Cayley_isog</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#13d63916ddaa339df3fcf04363ae7cde"><span class="id" title="notation">isog</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Cayley_repr"><span class="id" title="definition">Cayley_repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbitJ"><span class="id" title="lemma">orbitJ</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#30988ee242f08216f4b40cf90b42b816"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="orbitJ"><span class="id" title="lemma">orbitJ</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#38a288b01c62a2a6a720c34fc1fffe2c"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixJ"><span class="id" title="lemma">afixJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixJ"><span class="id" title="lemma">afixJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabJ"><span class="id" title="lemma">astabJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabJ"><span class="id" title="lemma">astabJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1J"><span class="id" title="lemma">astab1J</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#b59c327df8172426dc1fbd94c21cf201"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#b59c327df8172426dc1fbd94c21cf201"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#b59c327df8172426dc1fbd94c21cf201"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#b59c327df8172426dc1fbd94c21cf201"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1J"><span class="id" title="lemma">astab1J</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ca860d1e2e907b11919660f2c27c43e2"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ca860d1e2e907b11919660f2c27c43e2"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ca860d1e2e907b11919660f2c27c43e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ca860d1e2e907b11919660f2c27c43e2"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsJ"><span class="id" title="lemma">astabsJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsJ"><span class="id" title="lemma">astabsJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="setactJ"><span class="id" title="lemma">setactJ</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#495b9dab41eed2da7a7d91b1cb8498af"><span class="id" title="notation">^*</span></a>%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="setactJ"><span class="id" title="lemma">setactJ</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#1ebbed7bbef8371b25df9685ff0f4361"><span class="id" title="notation">^*</span></a>%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentJ"><span class="id" title="lemma">gacentJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#4ff57707e8e91cdc242380a7a9082e82"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#4ff57707e8e91cdc242380a7a9082e82"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentJ"><span class="id" title="lemma">gacentJ</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#a109fdcf21cc4aa5e2550ec2a3a49ee1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#a109fdcf21cc4aa5e2550ec2a3a49ee1"><span class="id" title="notation">J</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbitRs"><span class="id" title="lemma">orbitRs</span></a> <span class="id" title="var">G</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="orbitRs"><span class="id" title="lemma">orbitRs</span></a> <span class="id" title="var">G</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_afixRs_norms"><span class="id" title="lemma">sub_afixRs_norms</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#291276ea06db0b00a2747a79d012bbe0"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="sub_afixRs_norms"><span class="id" title="lemma">sub_afixRs_norms</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#667712f80037a604c35d3cc9930cac52"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_afixRs_norm"><span class="id" title="lemma">sub_afixRs_norm</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#291276ea06db0b00a2747a79d012bbe0"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="sub_afixRs_norm"><span class="id" title="lemma">sub_afixRs_norm</span></a> <span class="id" title="var">G</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#667712f80037a604c35d3cc9930cac52"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixRs_rcosets"><span class="id" title="lemma">afixRs_rcosets</span></a> <span class="id" title="var">A</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#35fe9120fe28e031e47d4f6cccd1bd3b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixRs_rcosets"><span class="id" title="lemma">afixRs_rcosets</span></a> <span class="id" title="var">A</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#71d97fc0a966da1de3f2bf32eada5367"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1Rs"><span class="id" title="lemma">astab1Rs</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1Rs"><span class="id" title="lemma">astab1Rs</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="actsRs_rcosets"><span class="id" title="lemma">actsRs_rcosets</span></a> <span class="id" title="var">H</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="actsRs_rcosets"><span class="id" title="lemma">actsRs_rcosets</span></a> <span class="id" title="var">H</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="transRs_rcosets"><span class="id" title="lemma">transRs_rcosets</span></a> <span class="id" title="var">H</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#ad5f1da050fedbae022d48bb21530fba"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="transRs_rcosets"><span class="id" title="lemma">transRs_rcosets</span></a> <span class="id" title="var">H</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">transitive</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a>.<br/> <br/> </div> @@ -2114,83 +2106,83 @@ This is the second part of Aschbacher (5.7) </div> <div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="astabRs_rcosets"><span class="id" title="lemma">astabRs_rcosets</span></a> <span class="id" title="var">H</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#45b5ed5ec521d3d65513a2c70294928a"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#gcore"><span class="id" title="definition">gcore</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabRs_rcosets"><span class="id" title="lemma">astabRs_rcosets</span></a> <span class="id" title="var">H</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#19e5d1024c73da4216b6b3643ffa31b6"><span class="id" title="notation">Rs</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#gcore"><span class="id" title="definition">gcore</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="orbitJs"><span class="id" title="lemma">orbitJs</span></a> <span class="id" title="var">G</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f05bcd008f250563fa67537a776ea961"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f05bcd008f250563fa67537a776ea961"><span class="id" title="notation">Js</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#6c121d1bcff5b1c0972474f398d18325"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="orbitJs"><span class="id" title="lemma">orbitJs</span></a> <span class="id" title="var">G</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.fingroup.action.html#22e8687cfe5bb55e5bdea729ad5c72c1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#22e8687cfe5bb55e5bdea729ad5c72c1"><span class="id" title="notation">Js</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#9034a9c14f90b74fd311ece73a2afd4b"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a>. <br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1Js"><span class="id" title="lemma">astab1Js</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f05bcd008f250563fa67537a776ea961"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f05bcd008f250563fa67537a776ea961"><span class="id" title="notation">Js</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1Js"><span class="id" title="lemma">astab1Js</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#22e8687cfe5bb55e5bdea729ad5c72c1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#22e8687cfe5bb55e5bdea729ad5c72c1"><span class="id" title="notation">Js</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="card_conjugates"><span class="id" title="lemma">card_conjugates</span></a> <span class="id" title="var">A</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#6c121d1bcff5b1c0972474f398d18325"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_conjugates"><span class="id" title="lemma">card_conjugates</span></a> <span class="id" title="var">A</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#9034a9c14f90b74fd311ece73a2afd4b"><span class="id" title="notation">:^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="afixJG"><span class="id" title="lemma">afixJG</span></a> <span class="id" title="var">G</span> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#cdd023ccc2efe92dd3cc3bafec9e78af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#cdd023ccc2efe92dd3cc3bafec9e78af"><span class="id" title="notation">JG</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#ff32a55d89a82185d94af5720a5e1f63"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="afixJG"><span class="id" title="lemma">afixJG</span></a> <span class="id" title="var">G</span> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">Fix_</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#9cb8ec4e4ed9f2067382df1e9eea44f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#9cb8ec4e4ed9f2067382df1e9eea44f5"><span class="id" title="notation">JG</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#6bf2e649062877caeedf56407c974b94"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astab1JG"><span class="id" title="lemma">astab1JG</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#cdd023ccc2efe92dd3cc3bafec9e78af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#cdd023ccc2efe92dd3cc3bafec9e78af"><span class="id" title="notation">JG</span></a><a class="idref" href="mathcomp.fingroup.action.html#f5d78ca47c9779b162180a14b237bdf4"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astab1JG"><span class="id" title="lemma">astab1JG</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#9cb8ec4e4ed9f2067382df1e9eea44f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#9cb8ec4e4ed9f2067382df1e9eea44f5"><span class="id" title="notation">JG</span></a><a class="idref" href="mathcomp.fingroup.action.html#0bfe9e510ff7d53177796cf76ba5dbc3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="dom_qactJ"><span class="id" title="lemma">dom_qactJ</span></a> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3d89e389df5b2c87554b2b824e5fe7d1"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="dom_qactJ"><span class="id" title="lemma">dom_qactJ</span></a> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#qact_dom"><span class="id" title="definition">qact_dom</span></a> <a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#377b6ecd73fb385c9347e204fcf683ec"><span class="id" title="notation">J</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="qactJ"><span class="id" title="lemma">qactJ</span></a> <span class="id" title="var">H</span> (<span class="id" title="var">Hy</span> : <a class="idref" href="mathcomp.fingroup.quotient.html#coset_of"><span class="id" title="record">coset_of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a>) <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a>%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#Hy"><span class="id" title="variable">Hy</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Hy"><span class="id" title="variable">Hy</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#808c6b8e35e792f23899f360a21e4638"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Hy"><span class="id" title="variable">Hy</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a>%<span class="id" title="var">act</span> <a class="idref" href="mathcomp.fingroup.action.html#Hy"><span class="id" title="variable">Hy</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Hy"><span class="id" title="variable">Hy</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.fingroup.action.html#Hy"><span class="id" title="variable">Hy</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="actsQ"><span class="id" title="lemma">actsQ</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">H</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#4fabb88b896fd67dca370ff89a430b72"><span class="id" title="notation">]</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">acts</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#915e8fb7bcea89ddadab4deff6ea659e"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabsQ"><span class="id" title="lemma">astabsQ</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#f49be8276ad4d3d8f37fd1509306940d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabsQ"><span class="id" title="lemma">astabsQ</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#c0af106a0ada6310ccb2e8e8c7766282"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabQ"><span class="id" title="lemma">astabQ</span></a> <span class="id" title="var">H</span> <span class="id" title="var">Abar</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#619a2190d60a66179f3396458e2a09ae"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabQ"><span class="id" title="lemma">astabQ</span></a> <span class="id" title="var">H</span> <span class="id" title="var">Abar</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#320f70d30c9a649ec82642b364681418"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="sub_astabQ"><span class="id" title="lemma">sub_astabQ</span></a> <span class="id" title="var">A</span> <span class="id" title="var">H</span> <span class="id" title="var">Bbar</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Bbar"><span class="id" title="variable">Bbar</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Bbar"><span class="id" title="variable">Bbar</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Bbar"><span class="id" title="variable">Bbar</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Bbar"><span class="id" title="variable">Bbar</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="sub_astabQR"><span class="id" title="lemma">sub_astabQR</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">H</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#44ce2df89b693f6f5ca2acfcd54d16b4"><span class="id" title="notation">[~:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#44ce2df89b693f6f5ca2acfcd54d16b4"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#44ce2df89b693f6f5ca2acfcd54d16b4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#653e048e978e57b1e513b9d5de2caee6"><span class="id" title="notation">[~:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#653e048e978e57b1e513b9d5de2caee6"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#653e048e978e57b1e513b9d5de2caee6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="astabQR"><span class="id" title="lemma">astabQR</span></a> <span class="id" title="var">A</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#44ce2df89b693f6f5ca2acfcd54d16b4"><span class="id" title="notation">[~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#44ce2df89b693f6f5ca2acfcd54d16b4"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#44ce2df89b693f6f5ca2acfcd54d16b4"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="astabQR"><span class="id" title="lemma">astabQR</span></a> <span class="id" title="var">A</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#653e048e978e57b1e513b9d5de2caee6"><span class="id" title="notation">[~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#653e048e978e57b1e513b9d5de2caee6"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#653e048e978e57b1e513b9d5de2caee6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="quotient_astabQ"><span class="id" title="lemma">quotient_astabQ</span></a> <span class="id" title="var">H</span> <span class="id" title="var">Abar</span> : <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="quotient_astabQ"><span class="id" title="lemma">quotient_astabQ</span></a> <span class="id" title="var">H</span> <span class="id" title="var">Abar</span> : <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#Abar"><span class="id" title="variable">Abar</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="conj_astabQ"><span class="id" title="lemma">conj_astabQ</span></a> <span class="id" title="var">A</span> <span class="id" title="var">H</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#b45e3930d72b4fd3a2651cb590e50b50"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#99d10685ba0de4584ba3a66908e81722"><span class="id" title="notation">)</span></a>.<br/> + <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#f8cc9e9a87e2166483438ca61952b8a4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#563ec7f167b9e19c804c7f8a07d81e1d"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="InternalGroupAction.CardClass"><span class="id" title="section">CardClass</span></a>.<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="index_cent1"><span class="id" title="lemma">index_cent1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#30988ee242f08216f4b40cf90b42b816"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="index_cent1"><span class="id" title="lemma">index_cent1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#38a288b01c62a2a6a720c34fc1fffe2c"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="classes_partition"><span class="id" title="lemma">classes_partition</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#classes"><span class="id" title="definition">classes</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="sum_card_class"><span class="id" title="lemma">sum_card_class</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">(</span></a><span class="id" title="var">C</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#classes"><span class="id" title="definition">classes</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="sum_card_class"><span class="id" title="lemma">sum_card_class</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">(</span></a><span class="id" title="var">C</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#classes"><span class="id" title="definition">classes</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="class_formula"><span class="id" title="lemma">class_formula</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">(</span></a><span class="id" title="var">C</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#classes"><span class="id" title="definition">classes</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#537ae7c18e428d4642a9dfb8520f03ee"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#addacbae2e0ffbfd03aaa03c308b39d7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="class_formula"><span class="id" title="lemma">class_formula</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">(</span></a><span class="id" title="var">C</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#classes"><span class="id" title="definition">classes</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> <a class="idref" href="mathcomp.fingroup.action.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#bb1f7e576b21e943bdeacc0f6a28b245"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="abelian_classP"><span class="id" title="lemma">abelian_classP</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#30988ee242f08216f4b40cf90b42b816"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b08e42f5c9c65aa9346e7b6dc26e3b5a"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a>).<br/> +<span class="id" title="keyword">Lemma</span> <a name="abelian_classP"><span class="id" title="lemma">abelian_classP</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#38a288b01c62a2a6a720c34fc1fffe2c"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="card_classes_abelian"><span class="id" title="lemma">card_classes_abelian</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#classes"><span class="id" title="definition">classes</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_classes_abelian"><span class="id" title="lemma">card_classes_abelian</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#classes"><span class="id" title="definition">classes</span></a> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction.CardClass"><span class="id" title="section">CardClass</span></a>.<br/> @@ -2199,21 +2191,21 @@ <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#InternalGroupAction"><span class="id" title="section">InternalGroupAction</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="gacentQ"><span class="id" title="lemma">gacentQ</span></a> (<span class="id" title="var">gT</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#a18f700a73b74a8543514202563c13c4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#a18f700a73b74a8543514202563c13c4"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#e2bbaaa2e35f8e6b75a00840566c57d7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="gacentQ"><span class="id" title="lemma">gacentQ</span></a> (<span class="id" title="var">gT</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">C_</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">(|</span></a><a class="idref" href="mathcomp.fingroup.action.html#7dcafbe20414081f1fadfdd82eb4964c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#7dcafbe20414081f1fadfdd82eb4964c"><span class="id" title="notation">Q</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.action.html#759306ed561fe32883e7922c4926d86c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.fingroup.action.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.fingroup.action.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="AutAct"><span class="id" title="section">AutAct</span></a>.<br/> <br/> -<span class="id" title="keyword">Variable</span> (<a name="AutAct.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="AutAct.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> +<span class="id" title="keyword">Variable</span> (<a name="AutAct.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="AutAct.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.fingroup.action.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="autact"><span class="id" title="definition">autact</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="projection">act</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#6e357cd64401db5e610bc455a18fd25f"><span class="id" title="notation">P</span></a> <a class="idref" href="mathcomp.fingroup.action.html#8328eb29c76b92b5b9da5590d036317b"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#subsetT"><span class="id" title="lemma">subsetT</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutAct.G"><span class="id" title="variable">G</span></a>)).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">aut_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#autact"><span class="id" title="definition">autact</span></a><a class="idref" href="mathcomp.fingroup.action.html#4f9e3ea32a2c10a2e344c72a4fd57c91"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="autact"><span class="id" title="definition">autact</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#act"><span class="id" title="projection">act</span></a> (<a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#3eb38e105ce23aabcb8ebe6af6d1b8af"><span class="id" title="notation">P</span></a> <a class="idref" href="mathcomp.fingroup.action.html#01828b84e5ef046de0f41b5eb7e81c3e"><span class="id" title="notation">\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#subsetT"><span class="id" title="lemma">subsetT</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#Aut"><span class="id" title="definition">Aut</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutAct.G"><span class="id" title="variable">G</span></a>)).<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">aut_action</span> := <a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.fingroup.action.html#autact"><span class="id" title="definition">autact</span></a><a class="idref" href="mathcomp.fingroup.action.html#ba40a15152c4d9ac6216da6c396077a5"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="autactK"><span class="id" title="lemma">autactK</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aut_action"><span class="id" title="definition">aut_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="autactK"><span class="id" title="lemma">autactK</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.fingroup.action.html#actperm"><span class="id" title="definition">actperm</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aut_action"><span class="id" title="definition">aut_action</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.action.html#a"><span class="id" title="variable">a</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="autact_is_groupAction"><span class="id" title="lemma">autact_is_groupAction</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <a class="idref" href="mathcomp.fingroup.action.html#AutAct.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.action.html#aut_action"><span class="id" title="definition">aut_action</span></a>.<br/> @@ -2223,8 +2215,8 @@ <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.fingroup.action.html#AutAct"><span class="id" title="section">AutAct</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="33eddbe1b49846aa9c1a4e3a43f0fe2f"><span class="id" title="notation">"</span></a>[ 'Aut' G ]" := (<a class="idref" href="mathcomp.fingroup.action.html#aut_action"><span class="id" title="definition">aut_action</span></a> <span class="id" title="var">G</span>) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="bbbd7c93723feb1df75c7fc60aa27b88"><span class="id" title="notation">"</span></a>[ 'Aut' G ]" := (<a class="idref" href="mathcomp.fingroup.action.html#aut_groupAction"><span class="id" title="definition">aut_groupAction</span></a> <span class="id" title="var">G</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="c6d4b1f79e75b84124452166fdbe2f47"><span class="id" title="notation">"</span></a>[ 'Aut' G ]" := (<a class="idref" href="mathcomp.fingroup.action.html#aut_action"><span class="id" title="definition">aut_action</span></a> <span class="id" title="var">G</span>) : <span class="id" title="var">action_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="f2aef07acd74cdfcf6ee224ab519cd4b"><span class="id" title="notation">"</span></a>[ 'Aut' G ]" := (<a class="idref" href="mathcomp.fingroup.action.html#aut_groupAction"><span class="id" title="definition">aut_groupAction</span></a> <span class="id" title="var">G</span>) : <span class="id" title="var">groupAction_scope</span>.<br/> <br/> </div> |