removing everything but index which redirects to the new page

author: Cyril Cohen 2019-10-16 11:26:43 +0200
committer: Cyril Cohen 2019-10-16 11:26:43 +0200
commit: 6b59540a2460633df4e3d8347cb4dfe2fb3a3afb (patch)
tree: 1239c1d5553d51a7d73f2f8b465f6a23178ff8a0 /docs/htmldoc/mathcomp.solvable.sylow.html
parent: dd82aaeae7e9478efc178ce8430986649555b032 (diff)
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-<head>
-<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<link href="coqdoc.css" rel="stylesheet" type="text/css" />
-<title>mathcomp.solvable.sylow</title>
-</head>
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-<body>
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-<div id="page">
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-<div id="main">
-
-<h1 class="libtitle">Library mathcomp.solvable.sylow</h1>
-
-<div class="code">
-<span class="comment">(*&nbsp;(c)&nbsp;Copyright&nbsp;2006-2016&nbsp;Microsoft&nbsp;Corporation&nbsp;and&nbsp;Inria.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br/>
-&nbsp;Distributed&nbsp;under&nbsp;the&nbsp;terms&nbsp;of&nbsp;CeCILL-B.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*)</span><br/>
-
-<br/>
-</div>
-
-<div class="doc">
-   The Sylow theorem and its consequences, including the Frattini argument, 
- the nilpotence of p-groups, and the Baer-Suzuki theorem.                   
-   This file also defines:                                                  
-      Zgroup G == G is a Z-group, i.e., has only cyclic Sylow p-subgroups.   
-</div>
-<div class="code">
-
-<br/>
-<span class="id" title="keyword">Set Implicit Arguments</span>.<br/>
-
-<br/>
-<span class="id" title="keyword">Import</span> <span class="id" title="var">GroupScope</span>.<br/>
-
-<br/>
-</div>
-
-<div class="doc">
- The mod p lemma for the action of p-groups.  
-</div>
-<div class="code">
-<span class="id" title="keyword">Section</span> <a name="ModP"><span class="id" title="section">ModP</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variable</span> (<a name="ModP.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="ModP.sT"><span class="id" title="variable">sT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="ModP.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.solvable.sylow.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">Variable</span> <a name="ModP.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.solvable.sylow.html#ModP.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#ModP.sT"><span class="id" title="variable">sT</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="pgroup_fix_mod"><span class="id" title="lemma">pgroup_fix_mod</span></a> (<span class="id" title="var">p</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</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.solvable.sylow.html#ModP.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.solvable.sylow.html#ModP.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/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#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.solvable.sylow.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.solvable.sylow.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.solvable.sylow.html#ModP.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.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.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#2b944e40a56cb605c3460196c2ed9ac4"><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#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.solvable.sylow.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.solvable.sylow.html#ModP.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.solvable.sylow.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="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#2b944e40a56cb605c3460196c2ed9ac4"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.div.html#2b944e40a56cb605c3460196c2ed9ac4"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.ssreflect.div.html#2b944e40a56cb605c3460196c2ed9ac4"><span class="id" title="notation">]</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#ModP"><span class="id" title="section">ModP</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Section</span> <a name="ModularGroupAction"><span class="id" title="section">ModularGroupAction</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variables</span> (<a name="ModularGroupAction.aT"><span class="id" title="variable">aT</span></a> <a name="ModularGroupAction.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="ModularGroupAction.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.solvable.sylow.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="ModularGroupAction.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.solvable.sylow.html#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/>
-<span class="id" title="keyword">Variables</span> (<a name="ModularGroupAction.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.solvable.sylow.html#ModularGroupAction.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction.R"><span class="id" title="variable">R</span></a>) (<a name="ModularGroupAction.p"><span class="id" title="variable">p</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</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.solvable.sylow.html#ModularGroupAction.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">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.solvable.sylow.html#ModularGroupAction.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="nontrivial_gacent_pgroup"><span class="id" title="lemma">nontrivial_gacent_pgroup</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#ModularGroupAction.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#M"><span class="id" title="variable">M</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.solvable.sylow.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.solvable.sylow.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.solvable.sylow.html#ModularGroupAction.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> <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/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#be2f022a539ec6d4d51932b5ea998e57"><span class="id" title="notation">:!=:</span></a> 1 <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#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.solvable.sylow.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.solvable.sylow.html#ModularGroupAction.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.solvable.sylow.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> <a class="idref" href="mathcomp.ssreflect.finset.html#be2f022a539ec6d4d51932b5ea998e57"><span class="id" title="notation">:!=:</span></a> 1.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="pcore_sub_astab_irr"><span class="id" title="lemma">pcore_sub_astab_irr</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#M"><span class="id" title="variable">M</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.solvable.sylow.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.solvable.sylow.html#ModularGroupAction.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#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction.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/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">O_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><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#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.solvable.sylow.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.solvable.sylow.html#ModularGroupAction.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="pcore_faithful_irr_act"><span class="id" title="lemma">pcore_faithful_irr_act</span></a> <span class="id" title="var">G</span> <span class="id" title="var">M</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#M"><span class="id" title="variable">M</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.solvable.sylow.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.solvable.sylow.html#ModularGroupAction.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#acts_irreducibly"><span class="id" title="definition">acts_irreducibly</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction.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/>
-&nbsp;&nbsp;&nbsp;&nbsp;<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.solvable.sylow.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.solvable.sylow.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.fingroup.action.html#b33bbd7f4609361a5f6c220c33141a0c"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction.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><br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">O_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><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">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#ModularGroupAction"><span class="id" title="section">ModularGroupAction</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Section</span> <a name="Sylow"><span class="id" title="section">Sylow</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variables</span> (<a name="Sylow.p"><span class="id" title="variable">p</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) (<a name="Sylow.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="Sylow.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.solvable.sylow.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>).<br/>
-<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">P</span> <span class="id" title="var">Q</span> <span class="id" title="var">H</span> <span class="id" title="var">K</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.solvable.sylow.html#Sylow.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">Theorem</span> <a name="Sylow's_theorem"><span class="id" title="lemma">Sylow's_theorem</span></a> :<br/>
-&nbsp;&nbsp;<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">P</span>, <a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">max</span></a> <span class="id" title="var">P</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">subgroup</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><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.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">,</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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.solvable.sylow.html#Sylow.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.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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#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#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</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/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">∀</span> <span class="id" title="var">P</span>, <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#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.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.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.solvable.sylow.html#P"><span class="id" title="variable">P</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/>
-&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">&amp;</span></a>  <a class="idref" href="mathcomp.ssreflect.prime.html#prime"><span class="id" title="definition">prime</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.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#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.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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.ssreflect.div.html#e3d79e08e7e529cc9ef532e000103386"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.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%<span class="id" title="var">N</span><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="max_pgroup_Sylow"><span class="id" title="lemma">max_pgroup_Sylow</span></a> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">max</span></a> <span class="id" title="var">P</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">subgroup</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><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.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_superset"><span class="id" title="lemma">Sylow_superset</span></a> <span class="id" title="var">Q</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.solvable.sylow.html#Sylow.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.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">{</span></a><span class="id" title="var">P</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">:</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.solvable.sylow.html#Sylow.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 class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.solvable.sylow.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.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">}</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_exists"><span class="id" title="lemma">Sylow_exists</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">{</span></a><span class="id" title="var">P</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">:</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.solvable.sylow.html#Sylow.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 class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">}</span></a>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Syl_trans"><span class="id" title="lemma">Syl_trans</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.solvable.sylow.html#Sylow.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.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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#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#7ff4d7c306e2eb723a4b0e54810870ae"><span class="id" title="notation">]</span></a>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_trans"><span class="id" title="lemma">Sylow_trans</span></a> <span class="id" title="var">P</span> <span class="id" title="var">Q</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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">x</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.solvable.sylow.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.solvable.sylow.html#Sylow.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">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f0bbce9238fab3dd03626439080979a9"><span class="id" title="notation">:=:</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#x"><span class="id" title="variable">x</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_subJ"><span class="id" title="lemma">Sylow_subJ</span></a> <span class="id" title="var">P</span> <span class="id" title="var">Q</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.solvable.sylow.html#Sylow.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.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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/>
-&nbsp;&nbsp;<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">x</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.solvable.sylow.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.solvable.sylow.html#Sylow.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">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.solvable.sylow.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#x"><span class="id" title="variable">x</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_Jsub"><span class="id" title="lemma">Sylow_Jsub</span></a> <span class="id" title="var">P</span> <span class="id" title="var">Q</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.solvable.sylow.html#Sylow.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.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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/>
-&nbsp;&nbsp;<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">x</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.solvable.sylow.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.solvable.sylow.html#Sylow.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">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="card_Syl"><span class="id" title="lemma">card_Syl</span></a> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#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.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.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.solvable.sylow.html#P"><span class="id" title="variable">P</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="card_Syl_dvd"><span class="id" title="lemma">card_Syl_dvd</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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.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.solvable.sylow.html#Sylow.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_Syl_mod"><span class="id" title="lemma">card_Syl_mod</span></a> : <a class="idref" href="mathcomp.ssreflect.prime.html#prime"><span class="id" title="definition">prime</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.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#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.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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.ssreflect.div.html#e3d79e08e7e529cc9ef532e000103386"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.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%<span class="id" title="var">N</span>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Frattini_arg"><span class="id" title="lemma">Frattini_arg</span></a> <span class="id" title="var">H</span> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#Sylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Sylow.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow.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.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_H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</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#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#Sylow"><span class="id" title="section">Sylow</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Section</span> <a name="MoreSylow"><span class="id" title="section">MoreSylow</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variables</span> (<a name="MoreSylow.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="MoreSylow.p"><span class="id" title="variable">p</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</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> <span class="id" title="var">P</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.solvable.sylow.html#MoreSylow.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="Sylow_setI_normal"><span class="id" title="lemma">Sylow_setI_normal</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">P</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#MoreSylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#MoreSylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> (<a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>).<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="normal_sylowP"><span class="id" title="lemma">normal_sylowP</span></a> <span class="id" title="var">G</span> :<br/>
-&nbsp;&nbsp;<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#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">P</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">:</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.solvable.sylow.html#MoreSylow.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 class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#MoreSylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>)<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">Syl_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#2cfdfd6f05a28cf984c6e60aeed6378f"><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.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1%<span class="id" title="var">N</span>).<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="trivg_center_pgroup"><span class="id" title="lemma">trivg_center_pgroup</span></a> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.solvable.sylow.html#MoreSylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><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 <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.solvable.sylow.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f0bbce9238fab3dd03626439080979a9"><span class="id" title="notation">:=:</span></a> 1.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="p2group_abelian"><span class="id" title="lemma">p2group_abelian</span></a> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.solvable.sylow.html#MoreSylow.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.prime.html#logn"><span class="id" title="definition">logn</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#MoreSylow.p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</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#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> 2 <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.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="card_p2group_abelian"><span class="id" title="lemma">card_p2group_abelian</span></a> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.ssreflect.prime.html#prime"><span class="id" title="definition">prime</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#MoreSylow.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#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.solvable.sylow.html#P"><span class="id" title="variable">P</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.solvable.sylow.html#MoreSylow.p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">^</span></a> 2)%<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.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_transversal_gen"><span class="id" title="lemma">Sylow_transversal_gen</span></a> (<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.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.solvable.sylow.html#MoreSylow.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 class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">G</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<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="keyword">∀</span> <span class="id" title="var">P</span>, <a class="idref" href="mathcomp.solvable.sylow.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#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.solvable.sylow.html#T"><span class="id" title="variable">T</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.solvable.sylow.html#P"><span class="id" title="variable">P</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.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<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="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.solvable.sylow.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#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.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">pi</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><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#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">P</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.solvable.sylow.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#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.solvable.sylow.html#T"><span class="id" title="variable">T</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">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">&lt;&lt;</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">P</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">&gt;&gt;</span></a> <a class="idref" href="http://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.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_gen"><span class="id" title="lemma">Sylow_gen</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">&lt;&lt;</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ec4dd368465f0599cdb8c6e3313efc95"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ec4dd368465f0599cdb8c6e3313efc95"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ec4dd368465f0599cdb8c6e3313efc95"><span class="id" title="notation">(</span></a><span class="id" title="var">P</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ec4dd368465f0599cdb8c6e3313efc95"><span class="id" title="notation">:</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.solvable.sylow.html#MoreSylow.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 class="idref" href="mathcomp.ssreflect.finset.html#ec4dd368465f0599cdb8c6e3313efc95"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.pgroup.html#Sylow"><span class="id" title="definition">Sylow</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ec4dd368465f0599cdb8c6e3313efc95"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">&gt;&gt;</span></a> <a class="idref" href="http://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.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#MoreSylow"><span class="id" title="section">MoreSylow</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Section</span> <a name="SomeHall"><span class="id" title="section">SomeHall</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variable</span> <a name="SomeHall.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">p</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) (<span class="id" title="var">pi</span> : <a class="idref" href="mathcomp.ssreflect.prime.html#nat_pred"><span class="id" title="definition">nat_pred</span></a>) (<span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> <span class="id" title="var">P</span> <span class="id" title="var">R</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.solvable.sylow.html#SomeHall.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="Hall_pJsub"><span class="id" title="lemma">Hall_pJsub</span></a> <span class="id" title="var">p</span> <span class="id" title="var">pi</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">P</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#pi"><span class="id" title="variable">pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">Hall</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.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#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.solvable.sylow.html#pi"><span class="id" title="variable">pi</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.solvable.sylow.html#P"><span class="id" title="variable">P</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.solvable.sylow.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.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <br/>
-&nbsp;&nbsp;<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">x</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.solvable.sylow.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.solvable.sylow.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">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#H"><span class="id" title="variable">H</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Hall_psubJ"><span class="id" title="lemma">Hall_psubJ</span></a> <span class="id" title="var">p</span> <span class="id" title="var">pi</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">P</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#pi"><span class="id" title="variable">pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">Hall</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.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#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.solvable.sylow.html#pi"><span class="id" title="variable">pi</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.solvable.sylow.html#P"><span class="id" title="variable">P</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.solvable.sylow.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.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <br/>
-&nbsp;&nbsp;<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">x</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.solvable.sylow.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.solvable.sylow.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">&amp;</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</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.solvable.sylow.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#x"><span class="id" title="variable">x</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Hall_setI_normal"><span class="id" title="lemma">Hall_setI_normal</span></a> <span class="id" title="var">pi</span> <span class="id" title="var">G</span> <span class="id" title="var">K</span> <span class="id" title="var">H</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#pi"><span class="id" title="variable">pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">Hall</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#pi"><span class="id" title="variable">pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">Hall</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">)</span></a> (<a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#K"><span class="id" title="variable">K</span></a>).<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="coprime_mulG_setI_norm"><span class="id" title="lemma">coprime_mulG_setI_norm</span></a> <span class="id" title="var">H</span> <span class="id" title="var">G</span> <span class="id" title="var">K</span> <span class="id" title="var">R</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.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.solvable.sylow.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.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><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.solvable.sylow.html#R"><span class="id" title="variable">R</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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><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.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><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.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#SomeHall"><span class="id" title="section">SomeHall</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Section</span> <a name="Nilpotent"><span class="id" title="section">Nilpotent</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variable</span> <a name="Nilpotent.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">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> <span class="id" title="var">P</span> <span class="id" title="var">L</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.solvable.sylow.html#Nilpotent.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">p</span> <span class="id" title="var">q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>).<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="pgroup_nil"><span class="id" title="lemma">pgroup_nil</span></a> <span class="id" title="var">p</span> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="pgroup_sol"><span class="id" title="lemma">pgroup_sol</span></a> <span class="id" title="var">p</span> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.nilpotent.html#solvable"><span class="id" title="definition">solvable</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="small_nil_class"><span class="id" title="lemma">small_nil_class</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.solvable.nilpotent.html#nil_class"><span class="id" title="definition">nil_class</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> 5 <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.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="nil_class2"><span class="id" title="lemma">nil_class2</span></a> <span class="id" title="var">G</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.solvable.nilpotent.html#nil_class"><span class="id" title="definition">nil_class</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> 2<a class="idref" href="http://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.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.commutator.html#5684e4e024467813e860f228f2381620"><span class="id" title="notation">^`(</span></a>1<a class="idref" href="mathcomp.solvable.commutator.html#5684e4e024467813e860f228f2381620"><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.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><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="nil_class3"><span class="id" title="lemma">nil_class3</span></a> <span class="id" title="var">G</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.solvable.nilpotent.html#nil_class"><span class="id" title="definition">nil_class</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> 3<a class="idref" href="http://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.solvable.nilpotent.html#e51b1b2b9737232f812351f799d286f3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.nilpotent.html#e51b1b2b9737232f812351f799d286f3"><span class="id" title="notation">L_3</span></a><a class="idref" href="mathcomp.solvable.nilpotent.html#e51b1b2b9737232f812351f799d286f3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.nilpotent.html#e51b1b2b9737232f812351f799d286f3"><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.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><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="nilpotent_maxp_normal"><span class="id" title="lemma">nilpotent_maxp_normal</span></a> <span class="id" title="var">pi</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">max</span></a> <span class="id" title="var">H</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#pi"><span class="id" title="variable">pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">subgroup</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#40070e138310190e4cd3ac9d3a86440d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#e6278be94ff3547a5d055628cea199c4"><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.solvable.sylow.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="nilpotent_Hall_pcore"><span class="id" title="lemma">nilpotent_Hall_pcore</span></a> <span class="id" title="var">pi</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#pi"><span class="id" title="variable">pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">Hall</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f0bbce9238fab3dd03626439080979a9"><span class="id" title="notation">:=:</span></a> <a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">O_pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">)</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="nilpotent_pcore_Hall"><span class="id" title="lemma">nilpotent_pcore_Hall</span></a> <span class="id" title="var">pi</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#pi"><span class="id" title="variable">pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">Hall</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#a4de5afc30e4046e35829de6f2bc75f3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">O_pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">)</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="nilpotent_pcoreC"><span class="id" title="lemma">nilpotent_pcoreC</span></a> <span class="id" title="var">pi</span> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">O_pi</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.fingroup.gproduct.html#191b5570f070a51bd5c860222c206828"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.gproduct.html#191b5570f070a51bd5c860222c206828"><span class="id" title="notation">x</span></a> <a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">O_pi</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#ca29ecf9a3780bf15fe608e2d2c00594"><span class="id" title="notation">^'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><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.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="sub_nilpotent_cent2"><span class="id" title="lemma">sub_nilpotent_cent2</span></a> <span class="id" title="var">H</span> <span class="id" title="var">K</span> <span class="id" title="var">G</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#K"><span class="id" title="variable">K</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.solvable.sylow.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.solvable.sylow.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.solvable.sylow.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.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><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.solvable.sylow.html#H"><span class="id" title="variable">H</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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#K"><span class="id" title="variable">K</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="pi_center_nilpotent"><span class="id" title="lemma">pi_center_nilpotent</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">pi</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><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.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">pi</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">)</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="Sylow_subnorm"><span class="id" title="lemma">Sylow_subnorm</span></a> <span class="id" title="var">p</span> <span class="id" title="var">G</span> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><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.solvable.sylow.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#Nilpotent"><span class="id" title="section">Nilpotent</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="nil_class_pgroup"><span class="id" title="lemma">nil_class_pgroup</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">p</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) (<span class="id" title="var">P</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.solvable.sylow.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>) :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.nilpotent.html#nil_class"><span class="id" title="definition">nil_class</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a> 1 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#f953bf7095e0da1cb644443fd0e17d6d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#logn"><span class="id" title="definition">logn</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#P"><span class="id" title="variable">P</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#f953bf7095e0da1cb644443fd0e17d6d"><span class="id" title="notation">).-1</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Definition</span> <a name="Zgroup"><span class="id" title="definition">Zgroup</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">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.solvable.sylow.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/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">∀</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">(</span></a><span class="id" title="var">V</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">:</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.solvable.sylow.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 class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.pgroup.html#Sylow"><span class="id" title="definition">Sylow</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#V"><span class="id" title="variable">V</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.cyclic.html#cyclic"><span class="id" title="definition">cyclic</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#V"><span class="id" title="variable">V</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">]</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Section</span> <a name="Zgroups"><span class="id" title="section">Zgroups</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variables</span> (<a name="Zgroups.gT"><span class="id" title="variable">gT</span></a> <a name="Zgroups.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="Zgroups.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.solvable.sylow.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="Zgroups.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.solvable.sylow.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">&gt;-&gt;</span></a> <a class="idref" href="mathcomp.solvable.sylow.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">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</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.solvable.sylow.html#Zgroups.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="ZgroupS"><span class="id" title="lemma">ZgroupS</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> : <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.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.solvable.sylow.html#Zgroup"><span class="id" title="definition">Zgroup</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#Zgroup"><span class="id" title="definition">Zgroup</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#H"><span class="id" title="variable">H</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="morphim_Zgroup"><span class="id" title="lemma">morphim_Zgroup</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.solvable.sylow.html#Zgroup"><span class="id" title="definition">Zgroup</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#Zgroup"><span class="id" title="definition">Zgroup</span></a> (<a class="idref" href="mathcomp.solvable.sylow.html#Zgroups.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.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>).<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="nil_Zgroup_cyclic"><span class="id" title="lemma">nil_Zgroup_cyclic</span></a> <span class="id" title="var">G</span> : <a class="idref" href="mathcomp.solvable.sylow.html#Zgroup"><span class="id" title="definition">Zgroup</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.nilpotent.html#nilpotent"><span class="id" title="definition">nilpotent</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.cyclic.html#cyclic"><span class="id" title="definition">cyclic</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#Zgroups"><span class="id" title="section">Zgroups</span></a>.<br/>
-
-<br/>
-
-<br/>
-<span class="id" title="keyword">Section</span> <a name="NilPGroups"><span class="id" title="section">NilPGroups</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Variables</span> (<a name="NilPGroups.p"><span class="id" title="variable">p</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) (<a name="NilPGroups.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">G</span> <span class="id" title="var">P</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.solvable.sylow.html#NilPGroups.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>
-
-<div class="doc">
- B &amp; G 1.22 p.9  
-</div>
-<div class="code">
-<span class="id" title="keyword">Lemma</span> <a name="normal_pgroup"><span class="id" title="lemma">normal_pgroup</span></a> <span class="id" title="var">r</span> <span class="id" title="var">P</span> <span class="id" title="var">N</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.html#NilPGroups.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.prime.html#logn"><span class="id" title="definition">logn</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#NilPGroups.p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#N"><span class="id" title="variable">N</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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<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">Q</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.solvable.sylow.html#NilPGroups.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 class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><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> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.solvable.sylow.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.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.solvable.sylow.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#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.sylow.html#Q"><span class="id" title="variable">Q</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.solvable.sylow.html#NilPGroups.p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#r"><span class="id" title="variable">r</span></a>)%<span class="id" title="var">N</span><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/>
-
-<br/>
-<span class="id" title="keyword">Theorem</span> <a name="Baer_Suzuki"><span class="id" title="lemma">Baer_Suzuki</span></a> <span class="id" title="var">x</span> <span class="id" title="var">G</span> :<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.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.solvable.sylow.html#NilPGroups.p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#15605b2ce8a0bd336aafa96c5cc1afdc"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">&lt;&lt;</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.solvable.sylow.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.sylow.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.solvable.sylow.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7fae3285ae0b14be2ed14c5a340c6d3d"><span class="id" title="notation">&gt;&gt;</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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.solvable.sylow.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.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">O_p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.sylow.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#64e6c9ddce70097e2cb88e9baa3b5a39"><span class="id" title="notation">)</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.sylow.html#NilPGroups"><span class="id" title="section">NilPGroups</span></a>.<br/>
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author	Cyril Cohen	2019-10-16 11:26:43 +0200
committer	Cyril Cohen	2019-10-16 11:26:43 +0200
commit	6b59540a2460633df4e3d8347cb4dfe2fb3a3afb (patch)
tree	1239c1d5553d51a7d73f2f8b465f6a23178ff8a0 /docs/htmldoc/mathcomp.solvable.sylow.html
parent	dd82aaeae7e9478efc178ce8430986649555b032 (diff)