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diff --git a/docs/htmldoc/mathcomp.solvable.burnside_app.html b/docs/htmldoc/mathcomp.solvable.burnside_app.html new file mode 100644 index 0000000..2e4ceb4 --- /dev/null +++ b/docs/htmldoc/mathcomp.solvable.burnside_app.html @@ -0,0 +1,927 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> +<link href="coqdoc.css" rel="stylesheet" type="text/css" /> +<title>mathcomp.solvable.burnside_app</title> +</head> + +<body> + +<div id="page"> + +<div id="header"> +</div> + +<div id="main"> + +<h1 class="libtitle">Library mathcomp.solvable.burnside_app</h1> + +<div class="code"> +<span class="comment">(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. <br/> + Distributed under the terms of CeCILL-B. *)</span><br/> +<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="mathcomp.ssreflect.ssreflect.html#"><span class="id" title="library">mathcomp.ssreflect.ssreflect</span></a>.<br/> + +<br/> +</div> + +<div class="doc"> + Application of the Burside formula to count the number of distinct + colorings of the vertices of a square and a cube. +</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/> +<span class="id" title="keyword">Lemma</span> <a name="burnside_formula"><span class="id" title="lemma">burnside_formula</span></a> : <span class="id" title="keyword">∀</span> (<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">s</span> (<span class="id" title="var">G</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>),<br/> + <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <span class="id" title="keyword">∀</span> (<span class="id" title="var">sT</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">to</span> : <a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">action</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#gT"><span class="id" title="variable">gT</span></a> <a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">&-></span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sT"><span class="id" title="variable">sT</span></a><a class="idref" href="mathcomp.fingroup.action.html#5c606fa2629c1fac8f3ee3f6e9ad2934"><span class="id" title="notation">}</span></a>),<br/> + (<a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#to"><span class="id" title="variable">to</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a>)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#b37dc668e343eb17a55a9974b7f85ec0"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#b37dc668e343eb17a55a9974b7f85ec0"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#b37dc668e343eb17a55a9974b7f85ec0"><span class="id" title="notation">(</span></a><span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#b37dc668e343eb17a55a9974b7f85ec0"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#b37dc668e343eb17a55a9974b7f85ec0"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> + +<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="colouring"><span class="id" title="section">colouring</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variable</span> <a name="colouring.n"><span class="id" title="variable">n</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">I_n</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">colors_eqType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">eqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">colors_choiceType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">choiceType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">colors_countType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">countType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">colors_finType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">finType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="colouring.square_colouring"><span class="id" title="section">square_colouring</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">I_4</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">square_eqType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">eqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">square_choiceType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">choiceType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">square_countType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">countType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">square_finType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">finType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">square_subType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">subType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">square_subCountType</span> :=<br/> + <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">subCountType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">square_subFinType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">subFinType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="mksquare"><span class="id" title="definition">mksquare</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#2179ac53e82aa7c0b2f2f5a16b5510ea"><span class="id" title="notation">%%</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.ssreflect.div.html#ltn_mod"><span class="id" title="lemma">ltn_mod</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#i"><span class="id" title="variable">i</span></a> 4).<br/> +<span class="id" title="keyword">Definition</span> <a name="c0"><span class="id" title="definition">c0</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mksquare"><span class="id" title="definition">mksquare</span></a> 0.<br/> +<span class="id" title="keyword">Definition</span> <a name="c1"><span class="id" title="definition">c1</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mksquare"><span class="id" title="definition">mksquare</span></a> 1.<br/> +<span class="id" title="keyword">Definition</span> <a name="c2"><span class="id" title="definition">c2</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mksquare"><span class="id" title="definition">mksquare</span></a> 2.<br/> +<span class="id" title="keyword">Definition</span> <a name="c3"><span class="id" title="definition">c3</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mksquare"><span class="id" title="definition">mksquare</span></a> 3.<br/> + +<br/> +</div> + +<div class="doc"> +rotations +</div> +<div class="code"> +<span class="id" title="keyword">Definition</span> <a name="R1"><span class="id" title="definition">R1</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="R2"><span class="id" title="definition">R2</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="R3"><span class="id" title="definition">R3</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Ltac</span> <span class="id" title="var">get_inv</span> <span class="id" title="var">elt</span> <span class="id" title="var">l</span> :=<br/> + <span class="id" title="keyword">match</span> <span class="id" title="var">l</span> <span class="id" title="keyword">with</span><br/> + | <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><span class="id" title="var">_</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><span class="id" title="var">elt</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> ?<span class="id" title="var">x</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">))</span></a> ⇒ <span class="id" title="var">x</span><br/> + | <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><span class="id" title="var">elt</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> ?<span class="id" title="var">x</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a> ⇒ <span class="id" title="var">x</span><br/> + | <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a>?<span class="id" title="var">x</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <span class="id" title="var">_</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a> ⇒ <span class="id" title="var">get_inv</span> <span class="id" title="var">elt</span> <span class="id" title="var">x</span><br/> + <span class="id" title="keyword">end</span>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="rot_inv"><span class="id" title="definition">rot_inv</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">((</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#R1"><span class="id" title="definition">R1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R3"><span class="id" title="definition">R3</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">),</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#R2"><span class="id" title="definition">R2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R2"><span class="id" title="definition">R2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">),</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#R3"><span class="id" title="definition">R3</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R1"><span class="id" title="definition">R1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">))</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Ltac</span> <span class="id" title="var">inj_tac</span> :=<br/> + <span class="id" title="tactic">move</span>: (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#erefl"><span class="id" title="abbreviation">erefl</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#rot_inv"><span class="id" title="definition">rot_inv</span></a>); <span class="id" title="tactic">unfold</span> <a class="idref" href="mathcomp.solvable.burnside_app.html#rot_inv"><span class="id" title="definition">rot_inv</span></a>;<br/> + <span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span> |- ?<span class="id" title="var">X</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> ?<span class="id" title="var">Y</span> ⇒<br/> + <span class="id" title="tactic">move</span>⇒ <span class="id" title="var">_</span>; <span class="id" title="keyword">let</span> <span class="id" title="var">x</span> := <span class="id" title="var">get_inv</span> <span class="id" title="var">Y</span> <span class="id" title="var">X</span> <span class="id" title="tactic">in</span><br/> + <span class="id" title="tactic">apply</span>: (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#can_inj"><span class="id" title="lemma">can_inj</span></a> (<span class="id" title="var">g</span>:=<span class="id" title="var">x</span>)); <span class="id" title="tactic">move</span>⇒ [<span class="id" title="var">val</span> <span class="id" title="var">H1</span>]<br/> + <span class="id" title="keyword">end</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R1_inj"><span class="id" title="lemma">R1_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R1"><span class="id" title="definition">R1</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R2_inj"><span class="id" title="lemma">R2_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R2"><span class="id" title="definition">R2</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R3_inj"><span class="id" title="lemma">R3_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R3"><span class="id" title="definition">R3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="r1"><span class="id" title="definition">r1</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R1_inj"><span class="id" title="lemma">R1_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r2"><span class="id" title="definition">r2</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R2_inj"><span class="id" title="lemma">R2_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r3"><span class="id" title="definition">r3</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R3_inj"><span class="id" title="lemma">R3_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="id1"><span class="id" title="definition">id1</span></a> := (1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="is_rot"><span class="id" title="definition">is_rot</span></a> (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>) := (<a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="rot"><span class="id" title="definition">rot</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">r</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#is_rot"><span class="id" title="definition">is_rot</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_rot"><span class="id" title="lemma">group_set_rot</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#rot"><span class="id" title="definition">rot</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rot_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#group_set_rot"><span class="id" title="lemma">group_set_rot</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="rotations"><span class="id" title="definition">rotations</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#id1"><span class="id" title="definition">id1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r2"><span class="id" title="definition">r2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r3"><span class="id" title="definition">r3</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="rot_eq_c0"><span class="id" title="lemma">rot_eq_c0</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">r</span> <span class="id" title="var">s</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>,<br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#is_rot"><span class="id" title="definition">is_rot</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#is_rot"><span class="id" title="definition">is_rot</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="rot_r1"><span class="id" title="lemma">rot_r1</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">r</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#is_rot"><span class="id" title="definition">is_rot</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#86a04fb564fb97d388cad84a3a204260"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#86a04fb564fb97d388cad84a3a204260"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#86a04fb564fb97d388cad84a3a204260"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="rotations_is_rot"><span class="id" title="lemma">rotations_is_rot</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">r</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#rotations"><span class="id" title="definition">rotations</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#is_rot"><span class="id" title="definition">is_rot</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="rot_is_rot"><span class="id" title="lemma">rot_is_rot</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#rot"><span class="id" title="definition">rot</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#rotations"><span class="id" title="definition">rotations</span></a>.<br/> + +<br/> +</div> + +<div class="doc"> +symmetries +</div> +<div class="code"> +<span class="id" title="keyword">Definition</span> <a name="Sh"><span class="id" title="definition">Sh</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Sh_inj"><span class="id" title="lemma">Sh_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sh"><span class="id" title="definition">Sh</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="sh"><span class="id" title="definition">sh</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sh_inj"><span class="id" title="lemma">Sh_inj</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sh_inv"><span class="id" title="lemma">sh_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#sh"><span class="id" title="definition">sh</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sh"><span class="id" title="definition">sh</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="Sv"><span class="id" title="definition">Sv</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Sv_inj"><span class="id" title="lemma">Sv_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sv"><span class="id" title="definition">Sv</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="sv"><span class="id" title="definition">sv</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sv_inj"><span class="id" title="lemma">Sv_inj</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sv_inv"><span class="id" title="lemma">sv_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#sv"><span class="id" title="definition">sv</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sv"><span class="id" title="definition">sv</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="Sd1"><span class="id" title="definition">Sd1</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Sd1_inj"><span class="id" title="lemma">Sd1_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sd1"><span class="id" title="definition">Sd1</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="sd1"><span class="id" title="definition">sd1</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sd1_inj"><span class="id" title="lemma">Sd1_inj</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sd1_inv"><span class="id" title="lemma">sd1_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#sd1"><span class="id" title="definition">sd1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sd1"><span class="id" title="definition">sd1</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="Sd2"><span class="id" title="definition">Sd2</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Sd2_inj"><span class="id" title="lemma">Sd2_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sd2"><span class="id" title="definition">Sd2</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="sd2"><span class="id" title="definition">sd2</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#Sd2_inj"><span class="id" title="lemma">Sd2_inj</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sd2_inv"><span class="id" title="lemma">sd2_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#sd2"><span class="id" title="definition">sd2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sd2"><span class="id" title="definition">sd2</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="ord_enum4"><span class="id" title="lemma">ord_enum4</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#enum"><span class="id" title="abbreviation">enum</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">I_4</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="diff_id_sh"><span class="id" title="lemma">diff_id_sh</span></a> : 1 <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sh"><span class="id" title="definition">sh</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="isometries2"><span class="id" title="definition">isometries2</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">set</span></a> 1<a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sh"><span class="id" title="definition">sh</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_iso2"><span class="id" title="lemma">card_iso2</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#isometries2"><span class="id" title="definition">isometries2</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 2.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_iso2"><span class="id" title="lemma">group_set_iso2</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#isometries2"><span class="id" title="definition">isometries2</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">iso2_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#group_set_iso2"><span class="id" title="lemma">group_set_iso2</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="isometries"><span class="id" title="definition">isometries</span></a> :=<br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">[||</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r2"><span class="id" title="definition">r2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r3"><span class="id" title="definition">r3</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sh"><span class="id" title="definition">sh</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sv"><span class="id" title="definition">sv</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sd1"><span class="id" title="definition">sd1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sd2"><span class="id" title="definition">sd2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="opp"><span class="id" title="definition">opp</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>) := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#b96c5fac4ea7ac478a42dc9d76e9dbb3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="is_iso"><span class="id" title="definition">is_iso</span></a> (<span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>) := <span class="id" title="keyword">∀</span> <span class="id" title="var">ci</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#opp"><span class="id" title="definition">opp</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#ci"><span class="id" title="variable">ci</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#opp"><span class="id" title="definition">opp</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#ci"><span class="id" title="variable">ci</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="isometries_iso"><span class="id" title="lemma">isometries_iso</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#isometries"><span class="id" title="definition">isometries</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso"><span class="id" title="definition">is_iso</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Ltac</span> <span class="id" title="var">non_inj</span> <span class="id" title="var">p</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">heq1</span> <span class="id" title="var">heq2</span> :=<br/> +<span class="id" title="keyword">let</span> <span class="id" title="var">h1</span>:= <span class="id" title="tactic">fresh</span> "h1" <span class="id" title="tactic">in</span><br/> +(<span class="id" title="var">absurd</span> (<span class="id" title="var">p</span> <span class="id" title="var">a1</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="var">p</span> <span class="id" title="var">a2</span>); <span class="id" title="tactic">first</span> (<span class="id" title="tactic">by</span> <span class="id" title="tactic">red</span> ⇒ - <span class="id" title="var">h1</span>; <span class="id" title="tactic">move</span>: (<a class="idref" href="mathcomp.fingroup.perm.html#perm_inj"><span class="id" title="lemma">perm_inj</span></a> <span class="id" title="var">h1</span>));<br/> +<span class="id" title="tactic">by</span> <span class="id" title="tactic">rewrite</span> <span class="id" title="var">heq1</span> <span class="id" title="var">heq2</span>; <span class="id" title="tactic">apply</span>/<a class="idref" href="mathcomp.ssreflect.eqtype.html#eqP"><span class="id" title="lemma">eqP</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Ltac</span> <span class="id" title="var">is_isoPtac</span> <span class="id" title="var">p</span> <span class="id" title="var">f</span> <span class="id" title="var">e0</span> <span class="id" title="var">e1</span> <span class="id" title="var">e2</span> <span class="id" title="var">e3</span> :=<br/> + <span class="id" title="var">suff</span> ->: <span class="id" title="var">p</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="var">f</span> <span class="id" title="tactic">by</span> [<span class="id" title="tactic">rewrite</span> <a class="idref" href="mathcomp.ssreflect.finset.html#inE"><span class="id" title="definition">inE</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqxx"><span class="id" title="abbreviation">eqxx</span></a> ?<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#orbT"><span class="id" title="lemma">orbT</span></a>];<br/> + <span class="id" title="keyword">let</span> <span class="id" title="var">e</span> := <span class="id" title="tactic">fresh</span> "e" <span class="id" title="tactic">in</span> <span class="id" title="tactic">apply</span>/<a class="idref" href="mathcomp.fingroup.perm.html#permP"><span class="id" title="lemma">permP</span></a>;<br/> + <span class="id" title="tactic">do</span> 5?[<span class="id" title="tactic">case</span>] ⇒ // ?; [<span class="id" title="tactic">move</span>: <span class="id" title="var">e0</span> | <span class="id" title="tactic">move</span>: <span class="id" title="var">e1</span> | <span class="id" title="tactic">move</span>: <span class="id" title="var">e2</span> | <span class="id" title="tactic">move</span>: <span class="id" title="var">e3</span>] ⇒ <span class="id" title="var">e</span>;<br/> + <span class="id" title="tactic">apply</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#etrans"><span class="id" title="definition">etrans</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#congr1"><span class="id" title="definition">congr1</span></a> <span class="id" title="var">p</span> <span class="id" title="var">_</span>) (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#etrans"><span class="id" title="definition">etrans</span></a> <span class="id" title="var">e</span> <span class="id" title="var">_</span>); <span class="id" title="tactic">apply</span>/<a class="idref" href="mathcomp.ssreflect.eqtype.html#eqP"><span class="id" title="lemma">eqP</span></a>; <span class="id" title="tactic">rewrite</span> // <a class="idref" href="mathcomp.fingroup.perm.html#permE"><span class="id" title="lemma">permE</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="is_isoP"><span class="id" title="lemma">is_isoP</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso"><span class="id" title="definition">is_iso</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a>) (<a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#isometries"><span class="id" title="definition">isometries</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_iso"><span class="id" title="lemma">group_set_iso</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#isometries"><span class="id" title="definition">isometries</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">iso_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#group_set_iso"><span class="id" title="lemma">group_set_iso</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_rot"><span class="id" title="lemma">card_rot</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#rot"><span class="id" title="definition">rot</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 4.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_rotations"><span class="id" title="lemma">group_set_rotations</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#rotations"><span class="id" title="definition">rotations</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rotations_group</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#group_set_rotations"><span class="id" title="lemma">group_set_rotations</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="col_squares"><span class="id" title="abbreviation">col_squares</span></a> := <a class="idref" href="mathcomp.ssreflect.finfun.html#9f24a6f16bf73832c2d9aa4e2c16f692"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#9f24a6f16bf73832c2d9aa4e2c16f692"><span class="id" title="notation">ffun</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#9f24a6f16bf73832c2d9aa4e2c16f692"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="act_f"><span class="id" title="definition">act_f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a>) (<span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a> :=<br/> + <a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">ffun</span></a> <span class="id" title="var">z</span> <a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">⇒</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a>)<a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="act_f_1"><span class="id" title="lemma">act_f_1</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">k</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#act_f"><span class="id" title="definition">act_f</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="act_f_morph"><span class="id" title="lemma">act_f_morph</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">k</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#act_f"><span class="id" title="definition">act_f</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#act_f"><span class="id" title="definition">act_f</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#act_f"><span class="id" title="definition">act_f</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="to"><span class="id" title="definition">to</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#TotalAction"><span class="id" title="definition">TotalAction</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#act_f_1"><span class="id" title="lemma">act_f_1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#act_f_morph"><span class="id" title="lemma">act_f_morph</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="square_coloring_number2"><span class="id" title="definition">square_coloring_number2</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#to"><span class="id" title="definition">to</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#isometries2"><span class="id" title="definition">isometries2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="square_coloring_number4"><span class="id" title="definition">square_coloring_number4</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#to"><span class="id" title="definition">to</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#rotations"><span class="id" title="definition">rotations</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="square_coloring_number8"><span class="id" title="definition">square_coloring_number8</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#to"><span class="id" title="definition">to</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#isometries"><span class="id" title="definition">isometries</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Fid"><span class="id" title="lemma">Fid</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_Fid"><span class="id" title="lemma">card_Fid</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">(</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#169c8da9095de246cb2051165c6767e3"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 4)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="coin0"><span class="id" title="definition">coin0</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="coin1"><span class="id" title="definition">coin1</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="coin2"><span class="id" title="definition">coin2</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="coin3"><span class="id" title="definition">coin3</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="eqperm_map"><span class="id" title="lemma">eqperm_map</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p1</span> <span class="id" title="var">p2</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a>,<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p2"><span class="id" title="variable">p2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#all"><span class="id" title="definition">all</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">s</span> ⇒ <a class="idref" href="mathcomp.solvable.burnside_app.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p2"><span class="id" title="variable">p2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a>) <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c0"><span class="id" title="definition">c0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c1"><span class="id" title="definition">c1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c2"><span class="id" title="definition">c2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#c3"><span class="id" title="definition">c3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_Sh"><span class="id" title="lemma">F_Sh</span></a> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#sh"><span class="id" title="definition">sh</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin0"><span class="id" title="definition">coin0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin3"><span class="id" title="definition">coin3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_Sv"><span class="id" title="lemma">F_Sv</span></a> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#sv"><span class="id" title="definition">sv</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin0"><span class="id" title="definition">coin0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin3"><span class="id" title="definition">coin3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Ltac</span> <span class="id" title="var">inv_tac</span> :=<br/> + <span class="id" title="tactic">apply</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#esym"><span class="id" title="definition">esym</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#etrans"><span class="id" title="definition">etrans</span></a> <span class="id" title="var">_</span> (<a class="idref" href="mathcomp.fingroup.fingroup.html#mul1g"><span class="id" title="lemma">mul1g</span></a> <span class="id" title="var">_</span>)); <span class="id" title="tactic">apply</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#canRL"><span class="id" title="lemma">canRL</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#mulgK"><span class="id" title="lemma">mulgK</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">_</span>;<br/> + <span class="id" title="keyword">let</span> <span class="id" title="var">a</span> := <span class="id" title="tactic">fresh</span> "a" <span class="id" title="tactic">in</span> <span class="id" title="tactic">apply</span>/<a class="idref" href="mathcomp.fingroup.perm.html#permP"><span class="id" title="lemma">permP</span></a> ⇒ <span class="id" title="var">a</span>;<br/> + <span class="id" title="tactic">apply</span>/<a class="idref" href="mathcomp.ssreflect.eqtype.html#eqP"><span class="id" title="lemma">eqP</span></a>; <span class="id" title="tactic">rewrite</span> <a class="idref" href="mathcomp.fingroup.perm.html#permM"><span class="id" title="lemma">permM</span></a> !<a class="idref" href="mathcomp.fingroup.perm.html#permE"><span class="id" title="lemma">permE</span></a>; <span class="id" title="tactic">case</span>: <span class="id" title="var">a</span>; <span class="id" title="tactic">do</span> 4?<span class="id" title="tactic">case</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="r1_inv"><span class="id" title="lemma">r1_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r3"><span class="id" title="definition">r3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="r2_inv"><span class="id" title="lemma">r2_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#r2"><span class="id" title="definition">r2</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r2"><span class="id" title="definition">r2</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="r3_inv"><span class="id" title="lemma">r3_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#r3"><span class="id" title="definition">r3</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r2"><span class="id" title="lemma">F_r2</span></a> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r2"><span class="id" title="definition">r2</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin0"><span class="id" title="definition">coin0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin3"><span class="id" title="definition">coin3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r1"><span class="id" title="lemma">F_r1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r1"><span class="id" title="definition">r1</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin0"><span class="id" title="definition">coin0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin3"><span class="id" title="definition">coin3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r3"><span class="id" title="lemma">F_r3</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r3"><span class="id" title="definition">r3</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin0"><span class="id" title="definition">coin0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin3"><span class="id" title="definition">coin3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_n2"><span class="id" title="lemma">card_n2</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">t</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>, <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 2)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_n"><span class="id" title="lemma">card_n</span></a> :<br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin0"><span class="id" title="definition">coin0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin3"><span class="id" title="definition">coin3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="burnside_app2"><span class="id" title="lemma">burnside_app2</span></a> : (<a class="idref" href="mathcomp.solvable.burnside_app.html#square_coloring_number2"><span class="id" title="definition">square_coloring_number2</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> 2 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 4 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 2)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="burnside_app_rot"><span class="id" title="lemma">burnside_app_rot</span></a> :<br/> + (<a class="idref" href="mathcomp.solvable.burnside_app.html#square_coloring_number4"><span class="id" title="definition">square_coloring_number4</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> 4 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 4 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 2 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 2 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a>)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_Sd1"><span class="id" title="lemma">F_Sd1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#sd1"><span class="id" title="definition">sd1</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin1"><span class="id" title="definition">coin1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin3"><span class="id" title="definition">coin3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_n3"><span class="id" title="lemma">card_n3</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#square"><span class="id" title="definition">square</span></a>, <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">set</span></a> <span class="id" title="var">k</span> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col_squares"><span class="id" title="abbreviation">col_squares</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 3)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_Sd2"><span class="id" title="lemma">F_Sd2</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#sd2"><span class="id" title="definition">sd2</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin0"><span class="id" title="definition">coin0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#coin2"><span class="id" title="definition">coin2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="burnside_app_iso"><span class="id" title="lemma">burnside_app_iso</span></a> :<br/> + (<a class="idref" href="mathcomp.solvable.burnside_app.html#square_coloring_number8"><span class="id" title="definition">square_coloring_number8</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> 8 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 4 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 2 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 3 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 3 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 2 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 2 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a>)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.square_colouring"><span class="id" title="section">square_colouring</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="colouring.cube_colouring"><span class="id" title="section">cube_colouring</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">I_6</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cube_eqType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">eqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cube_choiceType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">choiceType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cube_countType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">countType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#be2fb44e85835140c455bc256ce18d4c"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cube_finType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">finType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#eb1f7a25d8e03f1f02a5769831d0e74e"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cube_subType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">subType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cube_subCountType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">subCountType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#8a7192fa64a42310658fd5be07ae4fcc"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cube_subFinType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">subFinType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#a701c7b60b4a16f07950761d8bf90924"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="mkFcube"><span class="id" title="definition">mkFcube</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#2179ac53e82aa7c0b2f2f5a16b5510ea"><span class="id" title="notation">%%</span></a> 6) (<a class="idref" href="mathcomp.ssreflect.div.html#ltn_mod"><span class="id" title="lemma">ltn_mod</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#i"><span class="id" title="variable">i</span></a> 6).<br/> +<span class="id" title="keyword">Definition</span> <a name="F0"><span class="id" title="definition">F0</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mkFcube"><span class="id" title="definition">mkFcube</span></a> 0.<br/> +<span class="id" title="keyword">Definition</span> <a name="F1"><span class="id" title="definition">F1</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mkFcube"><span class="id" title="definition">mkFcube</span></a> 1.<br/> +<span class="id" title="keyword">Definition</span> <a name="F2"><span class="id" title="definition">F2</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mkFcube"><span class="id" title="definition">mkFcube</span></a> 2.<br/> +<span class="id" title="keyword">Definition</span> <a name="F3"><span class="id" title="definition">F3</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mkFcube"><span class="id" title="definition">mkFcube</span></a> 3.<br/> +<span class="id" title="keyword">Definition</span> <a name="F4"><span class="id" title="definition">F4</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mkFcube"><span class="id" title="definition">mkFcube</span></a> 4.<br/> +<span class="id" title="keyword">Definition</span> <a name="F5"><span class="id" title="definition">F5</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#mkFcube"><span class="id" title="definition">mkFcube</span></a> 5.<br/> + +<br/> +</div> + +<div class="doc"> + axial symetries +</div> +<div class="code"> +<span class="id" title="keyword">Definition</span> <a name="S05"><span class="id" title="definition">S05</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S05f"><span class="id" title="definition">S05f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S05"><span class="id" title="definition">S05</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="S14"><span class="id" title="definition">S14</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S14f"><span class="id" title="definition">S14f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S14"><span class="id" title="definition">S14</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="S23"><span class="id" title="definition">S23</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S23f"><span class="id" title="definition">S23f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S23"><span class="id" title="definition">S23</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +</div> + +<div class="doc"> + rotations 90 +</div> +<div class="code"> +<span class="id" title="keyword">Definition</span> <a name="R05"><span class="id" title="definition">R05</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R05f"><span class="id" title="definition">R05f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R05"><span class="id" title="definition">R05</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R50"><span class="id" title="definition">R50</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R50f"><span class="id" title="definition">R50f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R50"><span class="id" title="definition">R50</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R14"><span class="id" title="definition">R14</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R14f"><span class="id" title="definition">R14f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R14"><span class="id" title="definition">R14</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R41"><span class="id" title="definition">R41</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R41f"><span class="id" title="definition">R41f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R41"><span class="id" title="definition">R41</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R23"><span class="id" title="definition">R23</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R23f"><span class="id" title="definition">R23f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R23"><span class="id" title="definition">R23</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R32"><span class="id" title="definition">R32</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R32f"><span class="id" title="definition">R32f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R32"><span class="id" title="definition">R32</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +</div> + +<div class="doc"> + rotations 120 +</div> +<div class="code"> +<span class="id" title="keyword">Definition</span> <a name="R024"><span class="id" title="definition">R024</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R024f"><span class="id" title="definition">R024f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R024"><span class="id" title="definition">R024</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R042"><span class="id" title="definition">R042</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R042f"><span class="id" title="definition">R042f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R042"><span class="id" title="definition">R042</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R012"><span class="id" title="definition">R012</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R012f"><span class="id" title="definition">R012f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R012"><span class="id" title="definition">R012</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R021"><span class="id" title="definition">R021</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R021f"><span class="id" title="definition">R021f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R021"><span class="id" title="definition">R021</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R031"><span class="id" title="definition">R031</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R031f"><span class="id" title="definition">R031f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R031"><span class="id" title="definition">R031</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R013"><span class="id" title="definition">R013</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R013f"><span class="id" title="definition">R013f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R013"><span class="id" title="definition">R013</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R043"><span class="id" title="definition">R043</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R043f"><span class="id" title="definition">R043f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R043"><span class="id" title="definition">R043</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R034"><span class="id" title="definition">R034</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="R034f"><span class="id" title="definition">R034f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R034"><span class="id" title="definition">R034</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +</div> + +<div class="doc"> + last symmetries +</div> +<div class="code"> +<span class="id" title="keyword">Definition</span> <a name="S1"><span class="id" title="definition">S1</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S1f"><span class="id" title="definition">S1f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S1"><span class="id" title="definition">S1</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S2"><span class="id" title="definition">S2</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S2f"><span class="id" title="definition">S2f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S2"><span class="id" title="definition">S2</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S3"><span class="id" title="definition">S3</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S3f"><span class="id" title="definition">S3f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S3"><span class="id" title="definition">S3</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S4"><span class="id" title="definition">S4</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S4f"><span class="id" title="definition">S4f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S4"><span class="id" title="definition">S4</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S5"><span class="id" title="definition">S5</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S5f"><span class="id" title="definition">S5f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S5"><span class="id" title="definition">S5</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S6"><span class="id" title="definition">S6</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S6f"><span class="id" title="definition">S6f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S6"><span class="id" title="definition">S6</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S1_inv"><span class="id" title="lemma">S1_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S1f"><span class="id" title="definition">S1f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S2_inv"><span class="id" title="lemma">S2_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S2f"><span class="id" title="definition">S2f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S3_inv"><span class="id" title="lemma">S3_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S3f"><span class="id" title="definition">S3f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S4_inv"><span class="id" title="lemma">S4_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S4f"><span class="id" title="definition">S4f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S5_inv"><span class="id" title="lemma">S5_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S5f"><span class="id" title="definition">S5f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S6_inv"><span class="id" title="lemma">S6_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S6f"><span class="id" title="definition">S6f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S05_inj"><span class="id" title="lemma">S05_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S05f"><span class="id" title="definition">S05f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S14_inj"><span class="id" title="lemma">S14_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S14f"><span class="id" title="definition">S14f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S23_inv"><span class="id" title="lemma">S23_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S23f"><span class="id" title="definition">S23f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R05_inj"><span class="id" title="lemma">R05_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R05f"><span class="id" title="definition">R05f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R14_inj"><span class="id" title="lemma">R14_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R14f"><span class="id" title="definition">R14f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R23_inj"><span class="id" title="lemma">R23_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R23f"><span class="id" title="definition">R23f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R50_inj"><span class="id" title="lemma">R50_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R50f"><span class="id" title="definition">R50f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R41_inj"><span class="id" title="lemma">R41_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R41f"><span class="id" title="definition">R41f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R32_inj"><span class="id" title="lemma">R32_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R32f"><span class="id" title="definition">R32f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R024_inj"><span class="id" title="lemma">R024_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R024f"><span class="id" title="definition">R024f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R042_inj"><span class="id" title="lemma">R042_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R042f"><span class="id" title="definition">R042f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R012_inj"><span class="id" title="lemma">R012_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R012f"><span class="id" title="definition">R012f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R021_inj"><span class="id" title="lemma">R021_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R021f"><span class="id" title="definition">R021f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R031_inj"><span class="id" title="lemma">R031_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R031f"><span class="id" title="definition">R031f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R013_inj"><span class="id" title="lemma">R013_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R013f"><span class="id" title="definition">R013f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R043_inj"><span class="id" title="lemma">R043_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R043f"><span class="id" title="definition">R043f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="R034_inj"><span class="id" title="lemma">R034_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R034f"><span class="id" title="definition">R034f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="id3"><span class="id" title="definition">id3</span></a> := 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="s05"><span class="id" title="definition">s05</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S05_inj"><span class="id" title="lemma">S05_inj</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="s14"><span class="id" title="definition">s14</span></a> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="s23"><span class="id" title="definition">s23</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S23_inv"><span class="id" title="lemma">S23_inv</span></a>)).<br/> +<span class="id" title="keyword">Definition</span> <a name="r05"><span class="id" title="definition">r05</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R05_inj"><span class="id" title="lemma">R05_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r14"><span class="id" title="definition">r14</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R14_inj"><span class="id" title="lemma">R14_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r23"><span class="id" title="definition">r23</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R23_inj"><span class="id" title="lemma">R23_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r50"><span class="id" title="definition">r50</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R50_inj"><span class="id" title="lemma">R50_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r41"><span class="id" title="definition">r41</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R41_inj"><span class="id" title="lemma">R41_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r32"><span class="id" title="definition">r32</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R32_inj"><span class="id" title="lemma">R32_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r024"><span class="id" title="definition">r024</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R024_inj"><span class="id" title="lemma">R024_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r042"><span class="id" title="definition">r042</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R042_inj"><span class="id" title="lemma">R042_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r012"><span class="id" title="definition">r012</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R012_inj"><span class="id" title="lemma">R012_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r021"><span class="id" title="definition">r021</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R021_inj"><span class="id" title="lemma">R021_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r031"><span class="id" title="definition">r031</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R031_inj"><span class="id" title="lemma">R031_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r013"><span class="id" title="definition">r013</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R013_inj"><span class="id" title="lemma">R013_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r043"><span class="id" title="definition">r043</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R043_inj"><span class="id" title="lemma">R043_inj</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="r034"><span class="id" title="definition">r034</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R034_inj"><span class="id" title="lemma">R034_inj</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="s1"><span class="id" title="definition">s1</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S1_inv"><span class="id" title="lemma">S1_inv</span></a>)).<br/> +<span class="id" title="keyword">Definition</span> <a name="s2"><span class="id" title="definition">s2</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S2_inv"><span class="id" title="lemma">S2_inv</span></a>)).<br/> +<span class="id" title="keyword">Definition</span> <a name="s3"><span class="id" title="definition">s3</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S3_inv"><span class="id" title="lemma">S3_inv</span></a>)).<br/> +<span class="id" title="keyword">Definition</span> <a name="s4"><span class="id" title="definition">s4</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S4_inv"><span class="id" title="lemma">S4_inv</span></a>)).<br/> +<span class="id" title="keyword">Definition</span> <a name="s5"><span class="id" title="definition">s5</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S5_inv"><span class="id" title="lemma">S5_inv</span></a>)).<br/> +<span class="id" title="keyword">Definition</span> <a name="s6"><span class="id" title="definition">s6</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S6_inv"><span class="id" title="lemma">S6_inv</span></a>)).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dir_iso3"><span class="id" title="definition">dir_iso3</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a><br/> +<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">[||</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#id3"><span class="id" title="definition">id3</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s05"><span class="id" title="definition">s05</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s14"><span class="id" title="definition">s14</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s23"><span class="id" title="definition">s23</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r05"><span class="id" title="definition">r05</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r14"><span class="id" title="definition">r14</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r23"><span class="id" title="definition">r23</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#r50"><span class="id" title="definition">r50</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r41"><span class="id" title="definition">r41</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r32"><span class="id" title="definition">r32</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r024"><span class="id" title="definition">r024</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r042"><span class="id" title="definition">r042</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r012"><span class="id" title="definition">r012</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r021"><span class="id" title="definition">r021</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#r031"><span class="id" title="definition">r031</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r013"><span class="id" title="definition">r013</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r043"><span class="id" title="definition">r043</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r034"><span class="id" title="definition">r034</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#s1"><span class="id" title="definition">s1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s2"><span class="id" title="definition">s2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s3"><span class="id" title="definition">s3</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s4"><span class="id" title="definition">s4</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s5"><span class="id" title="definition">s5</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s6"><span class="id" title="definition">s6</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dir_iso3l"><span class="id" title="definition">dir_iso3l</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#id3"><span class="id" title="definition">id3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s05"><span class="id" title="definition">s05</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s14"><span class="id" title="definition">s14</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s23"><span class="id" title="definition">s23</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r05"><span class="id" title="definition">r05</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r14"><span class="id" title="definition">r14</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r23"><span class="id" title="definition">r23</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r50"><span class="id" title="definition">r50</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r41"><span class="id" title="definition">r41</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#r32"><span class="id" title="definition">r32</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r024"><span class="id" title="definition">r024</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r042"><span class="id" title="definition">r042</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r012"><span class="id" title="definition">r012</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r021"><span class="id" title="definition">r021</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r031"><span class="id" title="definition">r031</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r013"><span class="id" title="definition">r013</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r043"><span class="id" title="definition">r043</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r034"><span class="id" title="definition">r034</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#s1"><span class="id" title="definition">s1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s2"><span class="id" title="definition">s2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s3"><span class="id" title="definition">s3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s4"><span class="id" title="definition">s4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s5"><span class="id" title="definition">s5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s6"><span class="id" title="definition">s6</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="S0"><span class="id" title="definition">S0</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="S0f"><span class="id" title="definition">S0f</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S0"><span class="id" title="definition">S0</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#a561cbd02120e729eb821f52665c6080"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="S0_inv"><span class="id" title="lemma">S0_inv</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S0f"><span class="id" title="definition">S0f</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="s0"><span class="id" title="definition">s0</span></a> := (<a class="idref" href="mathcomp.fingroup.perm.html#perm"><span class="id" title="abbreviation">perm</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#inv_inj"><span class="id" title="lemma">inv_inj</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S0_inv"><span class="id" title="lemma">S0_inv</span></a>)).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="is_iso3"><span class="id" title="definition">is_iso3</span></a> (<span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>) := <span class="id" title="keyword">∀</span> <span class="id" title="var">fi</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#fi"><span class="id" title="variable">fi</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#fi"><span class="id" title="variable">fi</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dir_iso_iso3"><span class="id" title="lemma">dir_iso_iso3</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso3"><span class="id" title="definition">is_iso3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="iso3_ndir"><span class="id" title="lemma">iso3_ndir</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso3"><span class="id" title="definition">is_iso3</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="sop"><span class="id" title="definition">sop</span></a> (<span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a>)).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sop_inj"><span class="id" title="lemma">sop_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="prod_tuple"><span class="id" title="definition">prod_tuple</span></a> (<span class="id" title="var">t1</span> <span class="id" title="var">t2</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>) :=<br/> + <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">n</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">I_6</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.seq.html#nth"><span class="id" title="definition">nth</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t2"><span class="id" title="variable">t2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#n"><span class="id" title="variable">n</span></a>) <a class="idref" href="mathcomp.solvable.burnside_app.html#t1"><span class="id" title="variable">t1</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sop_spec"><span class="id" title="lemma">sop_spec</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> (<span class="id" title="var">n0</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9de6d53cccc27f521f3ab56b38159140"><span class="id" title="notation">I_6</span></a>), <a class="idref" href="mathcomp.ssreflect.seq.html#nth"><span class="id" title="definition">nth</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.solvable.burnside_app.html#n0"><span class="id" title="variable">n0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#n0"><span class="id" title="variable">n0</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="prod_t_correct"><span class="id" title="lemma">prod_t_correct</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>),<br/> + (<a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="mathcomp.solvable.burnside_app.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#nth"><span class="id" title="definition">nth</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#prod_tuple"><span class="id" title="definition">prod_tuple</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a>)) <a class="idref" href="mathcomp.solvable.burnside_app.html#i"><span class="id" title="variable">i</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sop_morph"><span class="id" title="lemma">sop_morph</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#prod_tuple"><span class="id" title="definition">prod_tuple</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="ecubes"><span class="id" title="definition">ecubes</span></a> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="ecubes_def"><span class="id" title="lemma">ecubes_def</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#ecubes"><span class="id" title="definition">ecubes</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#enum"><span class="id" title="abbreviation">enum</span></a> (@<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predT"><span class="id" title="definition">predT</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="seq_iso_L"><span class="id" title="definition">seq_iso_L</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">];</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#S05"><span class="id" title="definition">S05</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S14"><span class="id" title="definition">S14</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S23"><span class="id" title="definition">S23</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R05"><span class="id" title="definition">R05</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R14"><span class="id" title="definition">R14</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R23"><span class="id" title="definition">R23</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R50"><span class="id" title="definition">R50</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R41"><span class="id" title="definition">R41</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R32"><span class="id" title="definition">R32</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#R024"><span class="id" title="definition">R024</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R042"><span class="id" title="definition">R042</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R012"><span class="id" title="definition">R012</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R021"><span class="id" title="definition">R021</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R031"><span class="id" title="definition">R031</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R013"><span class="id" title="definition">R013</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R043"><span class="id" title="definition">R043</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#R034"><span class="id" title="definition">R034</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#S1"><span class="id" title="definition">S1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S2"><span class="id" title="definition">S2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S3"><span class="id" title="definition">S3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S4"><span class="id" title="definition">S4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S5"><span class="id" title="definition">S5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#S6"><span class="id" title="definition">S6</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="seqs1"><span class="id" title="lemma">seqs1</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">f</span> <span class="id" title="var">injf</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> (<a class="idref" href="mathcomp.fingroup.perm.html#ed3415d539756427d396dbdd3cf8051f"><span class="id" title="notation">@</span></a><a class="idref" href="mathcomp.fingroup.perm.html#ed3415d539756427d396dbdd3cf8051f"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.fingroup.perm.html#ed3415d539756427d396dbdd3cf8051f"><span class="id" title="notation">_</span></a> <a class="idref" href="mathcomp.fingroup.perm.html#ed3415d539756427d396dbdd3cf8051f"><span class="id" title="notation">f</span></a> <a class="idref" href="mathcomp.fingroup.perm.html#ed3415d539756427d396dbdd3cf8051f"><span class="id" title="notation">injf</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#ecubes"><span class="id" title="definition">ecubes</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Lcorrect"><span class="id" title="lemma">Lcorrect</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#seq_iso_L"><span class="id" title="definition">seq_iso_L</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#id3"><span class="id" title="definition">id3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s05"><span class="id" title="definition">s05</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s14"><span class="id" title="definition">s14</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s23"><span class="id" title="definition">s23</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r05"><span class="id" title="definition">r05</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r14"><span class="id" title="definition">r14</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r23"><span class="id" title="definition">r23</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#r50"><span class="id" title="definition">r50</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r41"><span class="id" title="definition">r41</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r32"><span class="id" title="definition">r32</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r024"><span class="id" title="definition">r024</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r042"><span class="id" title="definition">r042</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r012"><span class="id" title="definition">r012</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r021"><span class="id" title="definition">r021</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r031"><span class="id" title="definition">r031</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r013"><span class="id" title="definition">r013</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r043"><span class="id" title="definition">r043</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r034"><span class="id" title="definition">r034</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#s1"><span class="id" title="definition">s1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s2"><span class="id" title="definition">s2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s3"><span class="id" title="definition">s3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s4"><span class="id" title="definition">s4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s5"><span class="id" title="definition">s5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s6"><span class="id" title="definition">s6</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="iso0_1"><span class="id" title="lemma">iso0_1</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3l"><span class="id" title="definition">dir_iso3l</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="L_iso"><span class="id" title="lemma">L_iso</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#seq_iso_L"><span class="id" title="definition">seq_iso_L</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="stable"><span class="id" title="lemma">stable</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="iso_eq_F0_F1"><span class="id" title="lemma">iso_eq_F0_F1</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">r</span> <span class="id" title="var">s</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>, <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="ndir_s0p"><span class="id" title="lemma">ndir_s0p</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="indir_iso3l"><span class="id" title="definition">indir_iso3l</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#mulg"><span class="id" title="definition">mulg</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a>) <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3l"><span class="id" title="definition">dir_iso3l</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="iso3l"><span class="id" title="definition">iso3l</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3l"><span class="id" title="definition">dir_iso3l</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#2ac9001c05ad5bd2f6d5f68e59f48fbb"><span class="id" title="notation">++</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#indir_iso3l"><span class="id" title="definition">indir_iso3l</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="seq_iso3_L"><span class="id" title="definition">seq_iso3_L</span></a> := <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sop"><span class="id" title="definition">sop</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#iso3l"><span class="id" title="definition">iso3l</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="eqperm"><span class="id" title="lemma">eqperm</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p1</span> <span class="id" title="var">p2</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>,<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p2"><span class="id" title="variable">p2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#all"><span class="id" title="definition">all</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">s</span> ⇒ <a class="idref" href="mathcomp.solvable.burnside_app.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p2"><span class="id" title="variable">p2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a>) <a class="idref" href="mathcomp.solvable.burnside_app.html#ecubes"><span class="id" title="definition">ecubes</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="iso_eq_F0_F1_F2"><span class="id" title="lemma">iso_eq_F0_F1_F2</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">r</span> <span class="id" title="var">s</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>, <a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso3"><span class="id" title="definition">is_iso3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso3"><span class="id" title="definition">is_iso3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Ltac</span> <span class="id" title="var">iso_tac</span> :=<br/> + <span class="id" title="keyword">let</span> <span class="id" title="var">a</span> := <span class="id" title="tactic">fresh</span> "a" <span class="id" title="tactic">in</span> <span class="id" title="tactic">apply</span>/<a class="idref" href="mathcomp.fingroup.perm.html#permP"><span class="id" title="lemma">permP</span></a> ⇒ <span class="id" title="var">a</span>;<br/> + <span class="id" title="tactic">apply</span>/<a class="idref" href="mathcomp.ssreflect.eqtype.html#eqP"><span class="id" title="lemma">eqP</span></a>; <span class="id" title="tactic">rewrite</span> !<a class="idref" href="mathcomp.fingroup.perm.html#permM"><span class="id" title="lemma">permM</span></a> !<a class="idref" href="mathcomp.fingroup.perm.html#permE"><span class="id" title="lemma">permE</span></a>; <span class="id" title="tactic">case</span>: <span class="id" title="var">a</span>; <span class="id" title="tactic">do</span> 6?<span class="id" title="tactic">case</span>.<br/> + +<br/> +<span class="id" title="keyword">Ltac</span> <span class="id" title="var">inv_tac</span> :=<br/> + <span class="id" title="tactic">apply</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#esym"><span class="id" title="definition">esym</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#etrans"><span class="id" title="definition">etrans</span></a> <span class="id" title="var">_</span> (<a class="idref" href="mathcomp.fingroup.fingroup.html#mul1g"><span class="id" title="lemma">mul1g</span></a> <span class="id" title="var">_</span>)); <span class="id" title="tactic">apply</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#canRL"><span class="id" title="lemma">canRL</span></a> (<a class="idref" href="mathcomp.fingroup.fingroup.html#mulgK"><span class="id" title="lemma">mulgK</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">_</span>; <span class="id" title="var">iso_tac</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dir_s0p"><span class="id" title="lemma">dir_s0p</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="is_iso3b"><span class="id" title="definition">is_iso3b</span></a> <span class="id" title="var">p</span> := (<a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s0"><span class="id" title="definition">s0</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a>).<br/> +<span class="id" title="keyword">Definition</span> <a name="iso3"><span class="id" title="definition">iso3</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso3b"><span class="id" title="definition">is_iso3b</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="is_iso3P"><span class="id" title="lemma">is_iso3P</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#is_iso3"><span class="id" title="definition">is_iso3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a>) (<a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#iso3"><span class="id" title="definition">iso3</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_iso3"><span class="id" title="lemma">group_set_iso3</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#iso3"><span class="id" title="definition">iso3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">iso_group3</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#group_set_iso3"><span class="id" title="lemma">group_set_iso3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="group_set_diso3"><span class="id" title="lemma">group_set_diso3</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">diso_group3</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#group_set_diso3"><span class="id" title="lemma">group_set_diso3</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="gen_diso3"><span class="id" title="lemma">gen_diso3</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#dir_iso3"><span class="id" title="definition">dir_iso3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r05"><span class="id" title="definition">r05</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r14"><span class="id" title="definition">r14</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d251cae482ceced9589c8a2b3df261e7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#d2263119ac2870c795428c0a326d9d52"><span class="id" title="notation">>></span></a>.<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="col_cubes"><span class="id" title="abbreviation">col_cubes</span></a> := <a class="idref" href="mathcomp.ssreflect.finfun.html#9f24a6f16bf73832c2d9aa4e2c16f692"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#9f24a6f16bf73832c2d9aa4e2c16f692"><span class="id" title="notation">ffun</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#9f24a6f16bf73832c2d9aa4e2c16f692"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="act_g"><span class="id" title="definition">act_g</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>) (<span class="id" title="var">p</span> : <a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">perm</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a><a class="idref" href="mathcomp.fingroup.perm.html#8787ba8c1ae558dde17e1bdb8427679e"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a> :=<br/> + <a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">ffun</span></a> <span class="id" title="var">z</span> <a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">⇒</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a>)<a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="act_g_1"><span class="id" title="lemma">act_g_1</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">k</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#act_g"><span class="id" title="definition">act_g</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="act_g_morph"><span class="id" title="lemma">act_g_morph</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">k</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.solvable.burnside_app.html#act_g"><span class="id" title="definition">act_g</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#169fb610eeaa28cebf8ec36928167473"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#act_g"><span class="id" title="definition">act_g</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#act_g"><span class="id" title="definition">act_g</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#k"><span class="id" title="variable">k</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="to_g"><span class="id" title="definition">to_g</span></a> := <a class="idref" href="mathcomp.fingroup.action.html#TotalAction"><span class="id" title="definition">TotalAction</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#act_g_1"><span class="id" title="lemma">act_g_1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#act_g_morph"><span class="id" title="lemma">act_g_morph</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="cube_coloring_number24"><span class="id" title="definition">cube_coloring_number24</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#orbit"><span class="id" title="definition">orbit</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#to_g"><span class="id" title="definition">to_g</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#diso_group3"><span class="id" title="definition">diso_group3</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f2bdcb40cf423bf8d54f091f6cec6964"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Fid3"><span class="id" title="lemma">Fid3</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_Fid3"><span class="id" title="lemma">card_Fid3</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a>1<a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 6)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="col0"><span class="id" title="definition">col0</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="col1"><span class="id" title="definition">col1</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="col2"><span class="id" title="definition">col2</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="col3"><span class="id" title="definition">col3</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="col4"><span class="id" title="definition">col4</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="col5"><span class="id" title="definition">col5</span></a> (<span class="id" title="var">sc</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>) : <a class="idref" href="mathcomp.solvable.burnside_app.html#colors"><span class="id" title="definition">colors</span></a> := <a class="idref" href="mathcomp.solvable.burnside_app.html#sc"><span class="id" title="variable">sc</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="eqperm_map2"><span class="id" title="lemma">eqperm_map2</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">p1</span> <span class="id" title="var">p2</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a>,<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p2"><span class="id" title="variable">p2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#all"><span class="id" title="definition">all</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">s</span> ⇒ <a class="idref" href="mathcomp.solvable.burnside_app.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p2"><span class="id" title="variable">p2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s"><span class="id" title="variable">s</span></a>) <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F0"><span class="id" title="definition">F0</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F1"><span class="id" title="definition">F1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F2"><span class="id" title="definition">F2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F3"><span class="id" title="definition">F3</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F4"><span class="id" title="definition">F4</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#F5"><span class="id" title="definition">F5</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="infE"><span class="id" title="abbreviation">infE</span></a> := (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#sameP"><span class="id" title="lemma">sameP</span></a> <a class="idref" href="mathcomp.fingroup.action.html#afix1P"><span class="id" title="lemma">afix1P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqP"><span class="id" title="lemma">eqP</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s05"><span class="id" title="lemma">F_s05</span></a> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s05"><span class="id" title="definition">s05</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s14"><span class="id" title="lemma">F_s14</span></a> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s14"><span class="id" title="definition">s14</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="r05_inv"><span class="id" title="lemma">r05_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#r05"><span class="id" title="definition">r05</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r50"><span class="id" title="definition">r50</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="r50_inv"><span class="id" title="lemma">r50_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#r50"><span class="id" title="definition">r50</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r05"><span class="id" title="definition">r05</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="r14_inv"><span class="id" title="lemma">r14_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#r14"><span class="id" title="definition">r14</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r41"><span class="id" title="definition">r41</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="r41_inv"><span class="id" title="lemma">r41_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#r41"><span class="id" title="definition">r41</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#r14"><span class="id" title="definition">r14</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="s23_inv"><span class="id" title="lemma">s23_inv</span></a> : <a class="idref" href="mathcomp.solvable.burnside_app.html#s23"><span class="id" title="definition">s23</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#s23"><span class="id" title="definition">s23</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s23"><span class="id" title="lemma">F_s23</span></a> :<br/> + <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s23"><span class="id" title="definition">s23</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r05"><span class="id" title="lemma">F_r05</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r05"><span class="id" title="definition">r05</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r50"><span class="id" title="lemma">F_r50</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r50"><span class="id" title="definition">r50</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r23"><span class="id" title="lemma">F_r23</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r23"><span class="id" title="definition">r23</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r32"><span class="id" title="lemma">F_r32</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r32"><span class="id" title="definition">r32</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r14"><span class="id" title="lemma">F_r14</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r14"><span class="id" title="definition">r14</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r41"><span class="id" title="lemma">F_r41</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r41"><span class="id" title="definition">r41</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r024"><span class="id" title="lemma">F_r024</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r024"><span class="id" title="definition">r024</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r042"><span class="id" title="lemma">F_r042</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r042"><span class="id" title="definition">r042</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r012"><span class="id" title="lemma">F_r012</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r012"><span class="id" title="definition">r012</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r021"><span class="id" title="lemma">F_r021</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r021"><span class="id" title="definition">r021</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r031"><span class="id" title="lemma">F_r031</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r031"><span class="id" title="definition">r031</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r013"><span class="id" title="lemma">F_r013</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r013"><span class="id" title="definition">r013</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r043"><span class="id" title="lemma">F_r043</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r043"><span class="id" title="definition">r043</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_r034"><span class="id" title="lemma">F_r034</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#r034"><span class="id" title="definition">r034</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s1"><span class="id" title="lemma">F_s1</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s1"><span class="id" title="definition">s1</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s2"><span class="id" title="lemma">F_s2</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s2"><span class="id" title="definition">s2</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s3"><span class="id" title="lemma">F_s3</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s3"><span class="id" title="definition">s3</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s4"><span class="id" title="lemma">F_s4</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s4"><span class="id" title="definition">s4</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s5"><span class="id" title="lemma">F_s5</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s5"><span class="id" title="definition">s5</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="F_s6"><span class="id" title="lemma">F_s6</span></a> : <a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">Fix_to_g</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#s6"><span class="id" title="definition">s6</span></a><a class="idref" href="mathcomp.fingroup.action.html#726946a87895fde82e79cb27daba28a9"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col0"><span class="id" title="definition">col0</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col3"><span class="id" title="definition">col3</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col1"><span class="id" title="definition">col1</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col4"><span class="id" title="definition">col4</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#col2"><span class="id" title="definition">col2</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col5"><span class="id" title="definition">col5</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="uniq4_uniq6"><span class="id" title="lemma">uniq4_uniq6</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">t</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>,<br/> + <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_n4"><span class="id" title="lemma">card_n4</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">t</span> : <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>, <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 4)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_n3_3"><span class="id" title="lemma">card_n3_3</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">t</span>: <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>, <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 3)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_n2_3"><span class="id" title="lemma">card_n2_3</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">t</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span>: <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>, <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 2)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="card_n3s"><span class="id" title="lemma">card_n3s</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">t</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span>: <a class="idref" href="mathcomp.solvable.burnside_app.html#cube"><span class="id" title="definition">cube</span></a>, <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#b2d6f6eec274c9f9919a378a42b5b183"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">set</span></a> <span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#col_cubes"><span class="id" title="abbreviation">col_cubes</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d086f256e0c3de938a1d3ad3965b5d4b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 3)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="burnside_app_iso3"><span class="id" title="lemma">burnside_app_iso3</span></a> :<br/> + (<a class="idref" href="mathcomp.solvable.burnside_app.html#cube_coloring_number24"><span class="id" title="definition">cube_coloring_number24</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> 24 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/> + <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 6 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 6 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 3 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 3 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 4 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 8 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 2<a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> 6 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 3)%<span class="id" title="var">N</span>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring.cube_colouring"><span class="id" title="section">cube_colouring</span></a>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.solvable.burnside_app.html#colouring"><span class="id" title="section">colouring</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Corollary</span> <a name="burnside_app_iso_3_3col"><span class="id" title="lemma">burnside_app_iso_3_3col</span></a>: <a class="idref" href="mathcomp.solvable.burnside_app.html#cube_coloring_number24"><span class="id" title="definition">cube_coloring_number24</span></a> 3 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 57.<br/> + +<br/> +<span class="id" title="keyword">Corollary</span> <a name="burnside_app_iso_2_4col"><span class="id" title="lemma">burnside_app_iso_2_4col</span></a>: <a class="idref" href="mathcomp.solvable.burnside_app.html#square_coloring_number8"><span class="id" title="definition">square_coloring_number8</span></a> 4 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 55.<br/> + +<br/> +</div> +</div> + +<div id="footer"> +<hr/><a href="index.html">Index</a><hr/>This page has been generated by <a href="http://coq.inria.fr/">coqdoc</a> +</div> + +</div> + +</body> +</html>
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