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diff --git a/docs/htmldoc/mathcomp.character.inertia.html b/docs/htmldoc/mathcomp.character.inertia.html deleted file mode 100644 index e3fece2..0000000 --- a/docs/htmldoc/mathcomp.character.inertia.html +++ /dev/null @@ -1,966 +0,0 @@ -<!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.character.inertia</title> -</head> - -<body> - -<div id="page"> - -<div id="header"> -</div> - -<div id="main"> - -<h1 class="libtitle">Library mathcomp.character.inertia</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/> - -<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> <span class="id" title="var">GRing.Theory</span> <span class="id" title="var">Num.Theory</span>.<br/> -<span class="id" title="keyword">Local Open</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">ring_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - This file contains the definitions and properties of inertia groups: - (phi ^ y)%CF == the y-conjugate of phi : 'CF(G), i.e., the class - function mapping x ^ y to phi x provided y normalises G. - We take (phi ^ y)%CF = phi when y \notin 'N(G). - (phi ^: G)%CF == the sequence of all distinct conjugates of phi : 'CF(H) - by all y in G. - 'I[phi] == the inertia group of phi : CF(H), i.e., the set of y - such that (phi ^ y)%CF = phi AND H :^ y = y. - 'I_G[phi] == the inertia group of phi in G, i.e., G :&: 'I[phi]. - conjg_Iirr i y == the index j : Iirr G such that ('chi_i ^ y)%CF = 'chi_j. - cfclass_Iirr G i == the image of G under conjg_Iirr i, i.e., the set of j - such that 'chi_j \in ('chi_i ^: G)%CF. - mul_Iirr i j == the index k such that 'chi_j * 'chi_i = 'chi[G]_k, - or 0 if 'chi_j * 'chi_i is reducible. - mul_mod_Iirr i j := mul_Iirr i (mod_Iirr j), for j : Iirr (G / H). -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Reserved Notation</span> "''I[' phi ]"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''I[' phi ]").<br/> -<span class="id" title="keyword">Reserved Notation</span> "''I_' G [ phi ]"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">G</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 2, <span class="id" title="var">format</span> "''I_' G [ phi ]").<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ConjDef"><span class="id" title="section">ConjDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ConjDef.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ConjDef.B"><span class="id" title="variable">B</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="ConjDef.y"><span class="id" title="variable">y</span></a> : <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a>) (<a name="ConjDef.phi"><span class="id" title="variable">phi</span></a> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Fact</span> <a name="cfConjg_subproof"><span class="id" title="lemma">cfConjg_subproof</span></a> :<br/> - <a class="idref" href="mathcomp.character.classfun.html#is_class_fun"><span class="id" title="definition">is_class_fun</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="abbreviation">G</span></a> <a class="idref" href="mathcomp.ssreflect.finfun.html#486743bb05c6aa8b9d64fd3cec29ee79"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#486743bb05c6aa8b9d64fd3cec29ee79"><span class="id" title="notation">ffun</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finfun.html#486743bb05c6aa8b9d64fd3cec29ee79"><span class="id" title="notation">⇒</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjDef.phi"><span class="id" title="variable">phi</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjDef.y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="abbreviation">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjDef.y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="mathcomp.ssreflect.finfun.html#486743bb05c6aa8b9d64fd3cec29ee79"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="cfConjg"><span class="id" title="definition">cfConjg</span></a> := <a class="idref" href="mathcomp.character.classfun.html#Cfun"><span class="id" title="definition">Cfun</span></a> 1 <a class="idref" href="mathcomp.character.inertia.html#cfConjg_subproof"><span class="id" title="lemma">cfConjg_subproof</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#ConjDef"><span class="id" title="section">ConjDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">"</span></a>f ^ y" := (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <span class="id" title="var">y</span> <span class="id" title="var">f</span>) : <span class="id" title="var">cfun_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Conj"><span class="id" title="section">Conj</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Conj.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="Conj.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgE"><span class="id" title="lemma">cfConjgE</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> (<a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a>)%<span class="id" title="var">g</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgEJ"><span class="id" title="lemma">cfConjgEJ</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> (<a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgEout"><span class="id" title="lemma">cfConjgEout</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgEin"><span class="id" title="lemma">cfConjgEin</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> (<span class="id" title="var">nGy</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>) :<br/> - (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfIsom"><span class="id" title="definition">cfIsom</span></a> (<a class="idref" href="mathcomp.fingroup.automorphism.html#norm_conj_isom"><span class="id" title="lemma">norm_conj_isom</span></a> <a class="idref" href="mathcomp.character.inertia.html#nGy"><span class="id" title="variable">nGy</span></a>) <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgMnorm"><span class="id" title="lemma">cfConjgMnorm</span></a> <span class="id" title="var">phi</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>, <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.inertia.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_id"><span class="id" title="lemma">cfConjg_id</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Isaacs' 6.1.b -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgM"><span class="id" title="lemma">cfConjgM</span></a> <span class="id" title="var">L</span> <span class="id" title="var">phi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>, <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.inertia.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgJ1"><span class="id" title="lemma">cfConjgJ1</span></a> <span class="id" title="var">phi</span> : (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> 1)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgK"><span class="id" title="lemma">cfConjgK</span></a> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgKV"><span class="id" title="lemma">cfConjgKV</span></a> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a>) (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg1"><span class="id" title="lemma">cfConjg1</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> 1%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> 1%<span class="id" title="var">g</span>.<br/> - -<br/> -<span class="id" title="keyword">Fact</span> <a name="cfConjg_is_linear"><span class="id" title="lemma">cfConjg_is_linear</span></a> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Linear.Exports.linear"><span class="id" title="abbreviation">linear</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/> - <span class="id" title="keyword">Canonical</span> <span class="id" title="var">cfConjg_additive</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Additive.Exports.Additive"><span class="id" title="abbreviation">Additive</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg_is_linear"><span class="id" title="lemma">cfConjg_is_linear</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cfConjg_linear</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Linear.Exports.AddLinear"><span class="id" title="abbreviation">AddLinear</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg_is_linear"><span class="id" title="lemma">cfConjg_is_linear</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_cfuniJ"><span class="id" title="lemma">cfConjg_cfuniJ</span></a> <span class="id" title="var">A</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">_A</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_cfuni"><span class="id" title="lemma">cfConjg_cfuni</span></a> <span class="id" title="var">A</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">_A</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#483aeb200c980494b369f3b9c18f042e"><span class="id" title="notation">_A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_cfun1"><span class="id" title="lemma">cfConjg_cfun1</span></a> <span class="id" title="var">y</span> : (1 <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Fact</span> <a name="cfConjg_is_multiplicative"><span class="id" title="lemma">cfConjg_is_multiplicative</span></a> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.RMorphism.Exports.multiplicative"><span class="id" title="abbreviation">multiplicative</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cfConjg_rmorphism</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.RMorphism.Exports.AddRMorphism"><span class="id" title="abbreviation">AddRMorphism</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg_is_multiplicative"><span class="id" title="lemma">cfConjg_is_multiplicative</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cfConjg_lrmorphism</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#d17433407f88fd9a1e0740e2eddd6566"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#d17433407f88fd9a1e0740e2eddd6566"><span class="id" title="notation">lrmorphism</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d17433407f88fd9a1e0740e2eddd6566"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#d17433407f88fd9a1e0740e2eddd6566"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_eq1"><span class="id" title="lemma">cfConjg_eq1</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a>(<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfAutConjg"><span class="id" title="lemma">cfAutConjg</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">u</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.classfun.html#cfAut"><span class="id" title="definition">cfAut</span></a> <a class="idref" href="mathcomp.character.inertia.html#u"><span class="id" title="variable">u</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.classfun.html#cfAut"><span class="id" title="definition">cfAut</span></a> <a class="idref" href="mathcomp.character.inertia.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conj_cfConjg"><span class="id" title="lemma">conj_cfConjg</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.classfun.html#b24325f513e9801012e6322700f34266"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.classfun.html#b24325f513e9801012e6322700f34266"><span class="id" title="notation">)^*</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#b24325f513e9801012e6322700f34266"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfker_conjg"><span class="id" title="lemma">cfker_conjg</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfker"><span class="id" title="definition">cfker</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfker"><span class="id" title="definition">cfker</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfDetConjg"><span class="id" title="lemma">cfDetConjg</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.character.html#cfDet"><span class="id" title="definition">cfDet</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.character.html#cfDet"><span class="id" title="definition">cfDet</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#Conj"><span class="id" title="section">Conj</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Inertia"><span class="id" title="section">Inertia</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="Inertia.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="inertia"><span class="id" title="definition">inertia</span></a> (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) := <br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Fact</span> <a name="group_set_inertia"><span class="id" title="lemma">group_set_inertia</span></a> (<span class="id" title="var">H</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#group_set"><span class="id" title="definition">group_set</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">inertia_group</span> <span class="id" title="var">H</span> <span class="id" title="var">phi</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#Group"><span class="id" title="constructor">Group</span></a> (@<a class="idref" href="mathcomp.character.inertia.html#group_set_inertia"><span class="id" title="lemma">group_set_inertia</span></a> <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>).<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="Inertia.G"><span class="id" title="variable">G</span></a> <a name="Inertia.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertiaJ"><span class="id" title="lemma">inertiaJ</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_valJ"><span class="id" title="lemma">inertia_valJ</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> (<a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#746f7e4d3218aa2699eefc064b513fc2"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - To disambiguate basic inclucion lemma names we capitalize Inertia for - lemmas concerning the localized inertia group 'I_G[phi]. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="Inertia_sub"><span class="id" title="lemma">Inertia_sub</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="norm_inertia"><span class="id" title="lemma">norm_inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_inertia"><span class="id" title="lemma">sub_inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="normal_inertia"><span class="id" title="lemma">normal_inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_Inertia"><span class="id" title="lemma">sub_Inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="norm_Inertia"><span class="id" title="lemma">norm_Inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="normal_Inertia"><span class="id" title="lemma">normal_Inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_eqE"><span class="id" title="lemma">cfConjg_eqE</span></a> <span class="id" title="var">phi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>, (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#z"><span class="id" title="variable">z</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#667712f80037a604c35d3cc9930cac52"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cent_sub_inertia"><span class="id" title="lemma">cent_sub_inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cent_sub_Inertia"><span class="id" title="lemma">cent_sub_Inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#04a5555c0db8685a27679a7e6af3f8c3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#04a5555c0db8685a27679a7e6af3f8c3"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#04a5555c0db8685a27679a7e6af3f8c3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#04a5555c0db8685a27679a7e6af3f8c3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="center_sub_Inertia"><span class="id" title="lemma">center_sub_Inertia</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.solvable.center.html#e90cc03a62af307fc4e121114703663b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conjg_inertia"><span class="id" title="lemma">conjg_inertia</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#049e6d4210dc2b8af76facf30c9d4dd6"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia0"><span class="id" title="lemma">inertia0</span></a> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a>0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_add"><span class="id" title="lemma">inertia_add</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_sum"><span class="id" title="lemma">inertia_sum</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.character.inertia.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Phi</span> : <a class="idref" href="mathcomp.character.inertia.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.inertia.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.inertia.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Phi"><span class="id" title="variable">Phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.inertia.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.inertia.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#Phi"><span class="id" title="variable">Phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_scale"><span class="id" title="lemma">inertia_scale</span></a> <span class="id" title="var">a</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_scale_nz"><span class="id" title="lemma">inertia_scale_nz</span></a> <span class="id" title="var">a</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_opp"><span class="id" title="lemma">inertia_opp</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia1"><span class="id" title="lemma">inertia1</span></a> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a>1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="Inertia1"><span class="id" title="lemma">Inertia1</span></a> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a>1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_mul"><span class="id" title="lemma">inertia_mul</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_prod"><span class="id" title="lemma">inertia_prod</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.character.inertia.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Phi</span> : <a class="idref" href="mathcomp.character.inertia.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.inertia.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.inertia.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Phi"><span class="id" title="variable">Phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#edca584f226f01d7a05a12e4ceba1caf"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#edca584f226f01d7a05a12e4ceba1caf"><span class="id" title="notation">prod_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#edca584f226f01d7a05a12e4ceba1caf"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#edca584f226f01d7a05a12e4ceba1caf"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.inertia.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#edca584f226f01d7a05a12e4ceba1caf"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.inertia.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#edca584f226f01d7a05a12e4ceba1caf"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#Phi"><span class="id" title="variable">Phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_injective"><span class="id" title="lemma">inertia_injective</span></a> (<span class="id" title="var">chi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_irr_prime"><span class="id" title="lemma">inertia_irr_prime</span></a> <span class="id" title="var">p</span> <span class="id" title="var">i</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.prime.html#prime"><span class="id" title="definition">prime</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#313ef60ac6c7566906fa5b28c1bbf405"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_irr0"><span class="id" title="lemma">inertia_irr0</span></a> : <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_0</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Isaacs' 6.1.c -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_iso"><span class="id" title="lemma">cfConjg_iso</span></a> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.classfun.html#isometry"><span class="id" title="definition">isometry</span></a> (<a class="idref" href="mathcomp.character.inertia.html#cfConjg"><span class="id" title="definition">cfConjg</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/> - -<br/> -</div> - -<div class="doc"> - Isaacs' 6.1.d -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="cfdot_Res_conjg"><span class="id" title="lemma">cfdot_Res_conjg</span></a> <span class="id" title="var">psi</span> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Isaac's 6.1.e -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_char"><span class="id" title="lemma">cfConjg_char</span></a> (<span class="id" title="var">chi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#character"><span class="id" title="definition">character</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#character"><span class="id" title="definition">character</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_lin_char"><span class="id" title="lemma">cfConjg_lin_char</span></a> (<span class="id" title="var">chi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#linear_char"><span class="id" title="definition">linear_char</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#linear_char"><span class="id" title="definition">linear_char</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjg_irr"><span class="id" title="lemma">cfConjg_irr</span></a> <span class="id" title="var">y</span> <span class="id" title="var">chi</span> : <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a> <span class="id" title="var">i</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.character.character.html#cfIirr"><span class="id" title="definition">cfIirr</span></a> (<a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conjg_IirrE"><span class="id" title="lemma">conjg_IirrE</span></a> <span class="id" title="var">i</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conjg_IirrK"><span class="id" title="lemma">conjg_IirrK</span></a> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a>%<span class="id" title="var">g</span>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conjg_IirrKV"><span class="id" title="lemma">conjg_IirrKV</span></a> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a>%<span class="id" title="var">g</span>) (<a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conjg_Iirr_inj"><span class="id" title="lemma">conjg_Iirr_inj</span></a> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> (<a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conjg_Iirr_eq0"><span class="id" title="lemma">conjg_Iirr_eq0</span></a> <span class="id" title="var">i</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="conjg_Iirr0"><span class="id" title="lemma">conjg_Iirr0</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a> 0 <a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 0.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfdot_irr_conjg"><span class="id" title="lemma">cfdot_irr_conjg</span></a> <span class="id" title="var">i</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#8c3a7a3fdf9f8133b80af549f7126572"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#8c3a7a3fdf9f8133b80af549f7126572"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.character.classfun.html#8c3a7a3fdf9f8133b80af549f7126572"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#8c3a7a3fdf9f8133b80af549f7126572"><span class="id" title="notation">_H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">)%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="cfclass"><span class="id" title="definition">cfclass</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) := <br/> - <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#repr"><span class="id" title="definition">repr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Tx"><span class="id" title="variable">Tx</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">Tx</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#rcosets"><span class="id" title="definition">rcosets</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_B</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">]</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="size_cfclass"><span class="id" title="lemma">size_cfclass</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> (<a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclassP"><span class="id" title="lemma">cfclassP</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">y</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> (<a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclassInorm"><span class="id" title="lemma">cfclassInorm</span></a> <span class="id" title="var">phi</span> : (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">N_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ee98cf35a816a182ecdf169a5f07c7f5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_refl"><span class="id" title="lemma">cfclass_refl</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_transr"><span class="id" title="lemma">cfclass_transr</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> :<br/> - (<a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_sym"><span class="id" title="lemma">cfclass_sym</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> : (<a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_uniq"><span class="id" title="lemma">cfclass_uniq</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_invariant"><span class="id" title="lemma">cfclass_invariant</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass1"><span class="id" title="lemma">cfclass1</span></a> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (1 <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">[::</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="cfclass_Iirr"><span class="id" title="definition">cfclass_Iirr</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">i</span> := <a class="idref" href="mathcomp.character.inertia.html#conjg_Iirr"><span class="id" title="definition">conjg_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_IirrE"><span class="id" title="lemma">cfclass_IirrE</span></a> <span class="id" title="var">i</span> <span class="id" title="var">j</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#cfclass_Iirr"><span class="id" title="definition">cfclass_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_cfclass_IirrE"><span class="id" title="lemma">eq_cfclass_IirrE</span></a> <span class="id" title="var">i</span> <span class="id" title="var">j</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#cfclass_Iirr"><span class="id" title="definition">cfclass_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.character.inertia.html#cfclass_Iirr"><span class="id" title="definition">cfclass_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#cfclass_Iirr"><span class="id" title="definition">cfclass_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="im_cfclass_Iirr"><span class="id" title="lemma">im_cfclass_Iirr</span></a> <span class="id" title="var">i</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#perm_eq"><span class="id" title="definition">perm_eq</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#cfclass_Iirr"><span class="id" title="definition">cfclass_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">]</span></a> (<a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="card_cfclass_Iirr"><span class="id" title="lemma">card_cfclass_Iirr</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#cfclass_Iirr"><span class="id" title="definition">cfclass_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#d7868928c9838e25cd788c180bafc9d3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="reindex_cfclass"><span class="id" title="lemma">reindex_cfclass</span></a> <span class="id" title="var">R</span> <span class="id" title="var">idx</span> (<span class="id" title="var">op</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">Monoid.com_law</span></a> <a class="idref" href="mathcomp.character.inertia.html#idx"><span class="id" title="variable">idx</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">i</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.character.inertia.html#idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">chi</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> (<a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.character.inertia.html#idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> (<a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfResInd"><span class="id" title="lemma">cfResInd</span></a> <span class="id" title="var">j</span>:<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> (<a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">(</span></a><span class="id" title="var">y</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem (6.2) -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="Clifford_Res_sum_cfclass"><span class="id" title="lemma">Clifford_Res_sum_cfclass</span></a> <span class="id" title="var">i</span> <span class="id" title="var">j</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <br/> - <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">chi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation"><-</span></a> (<a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfRes_Ind_invariant"><span class="id" title="lemma">cfRes_Ind_invariant</span></a> <span class="id" title="var">psi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#3ee2a1dd4ae14529933a33a195dedd6e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">('</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">H</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">psi</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Corollary (6.7). -</div> -<div class="code"> -<span class="id" title="keyword">Corollary</span> <a name="constt0_Res_cfker"><span class="id" title="lemma">constt0_Res_cfker</span></a> <span class="id" title="var">i</span> : <br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfker"><span class="id" title="definition">cfker</span></a> <a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Lemma (6.8). -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="dvdn_constt_Res1_irr1"><span class="id" title="lemma">dvdn_constt_Res1_irr1</span></a> <span class="id" title="var">i</span> <span class="id" title="var">j</span> : <br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">n</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> 1%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a> 1%<span class="id" title="var">g</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_Ind"><span class="id" title="lemma">cfclass_Ind</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#0df56e8239d8a380b545a76c4949b3d8"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#Inertia"><span class="id" title="section">Inertia</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">"</span></a>''I[' phi ] " := (<a class="idref" href="mathcomp.character.inertia.html#inertia"><span class="id" title="definition">inertia</span></a> <span class="id" title="var">phi</span>) : <span class="id" title="var">group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c4dc2d44ea48d5d7d27f43e6f582b0f4"><span class="id" title="notation">"</span></a>''I[' phi ] " := (<a class="idref" href="mathcomp.character.inertia.html#inertia_group"><span class="id" title="definition">inertia_group</span></a> <span class="id" title="var">phi</span>) : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">"</span></a>''I_' G [ phi ] " := (<span class="id" title="var">G</span>%<span class="id" title="var">g</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><span class="id" title="var">phi</span><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="62b458591c37f1e5f176500bb6809ae8"><span class="id" title="notation">"</span></a>''I_' G [ phi ] " := (<span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#83bfb527fd8c6ef7c38a16fb45f9e361"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.inertia.html#c4dc2d44ea48d5d7d27f43e6f582b0f4"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#c4dc2d44ea48d5d7d27f43e6f582b0f4"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#c4dc2d44ea48d5d7d27f43e6f582b0f4"><span class="id" title="notation">[</span></a><span class="id" title="var">phi</span><a class="idref" href="mathcomp.character.inertia.html#c4dc2d44ea48d5d7d27f43e6f582b0f4"><span class="id" title="notation">]</span></a>)%<span class="id" title="var">G</span> : <span class="id" title="var">Group_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="7eb4912ca81578db62a4b2170c23860a"><span class="id" title="notation">"</span></a>phi ^: G" := (<a class="idref" href="mathcomp.character.inertia.html#cfclass"><span class="id" title="definition">cfclass</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">G</span>) : <span class="id" title="var">cfun_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ConjRestrict"><span class="id" title="section">ConjRestrict</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ConjRestrict.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ConjRestrict.G"><span class="id" title="variable">G</span></a> <a name="ConjRestrict.H"><span class="id" title="variable">H</span></a> <a name="ConjRestrict.K"><span class="id" title="variable">K</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgRes_norm"><span class="id" title="lemma">cfConjgRes_norm</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">CF</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgRes"><span class="id" title="lemma">cfConjgRes</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">CF</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_inertia_Res"><span class="id" title="lemma">sub_inertia_Res</span></a> <span class="id" title="var">phi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgInd_norm"><span class="id" title="lemma">cfConjgInd_norm</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">CF</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgInd"><span class="id" title="lemma">cfConjgInd</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">CF</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_inertia_Ind"><span class="id" title="lemma">sub_inertia_Ind</span></a> <span class="id" title="var">phi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict"><span class="id" title="section">ConjRestrict</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="MoreInertia"><span class="id" title="section">MoreInertia</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="MoreInertia.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="MoreInertia.G"><span class="id" title="variable">G</span></a> <a name="MoreInertia.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="MoreInertia.i"><span class="id" title="variable">i</span></a> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a>).<br/> -<span class="id" title="keyword">Let</span> <a name="MoreInertia.T"><span class="id" title="variable">T</span></a> := <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_id"><span class="id" title="lemma">inertia_id</span></a> : <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_T</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#MoreInertia.T"><span class="id" title="variable">T</span></a>. <br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfclass_inertia"><span class="id" title="lemma">cfclass_inertia</span></a> : (<a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#MoreInertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#7eb4912ca81578db62a4b2170c23860a"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.character.inertia.html#MoreInertia.T"><span class="id" title="variable">T</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#MoreInertia"><span class="id" title="section">MoreInertia</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ConjMorph"><span class="id" title="section">ConjMorph</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ConjMorph.aT"><span class="id" title="variable">aT</span></a> <a name="ConjMorph.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ConjMorph.D"><span class="id" title="variable">D</span></a> <a name="ConjMorph.G"><span class="id" title="variable">G</span></a> <a name="ConjMorph.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="ConjMorph.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.character.inertia.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.character.inertia.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgMorph"><span class="id" title="lemma">cfConjgMorph</span></a> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#cfMorph"><span class="id" title="definition">cfMorph</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfMorph"><span class="id" title="definition">cfMorph</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_morph_pre"><span class="id" title="lemma">inertia_morph_pre</span></a> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfMorph"><span class="id" title="definition">cfMorph</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#320f70d30c9a649ec82642b364681418"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_morph_im"><span class="id" title="lemma">inertia_morph_im</span></a> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfMorph"><span class="id" title="definition">cfMorph</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ConjMorph.R"><span class="id" title="variable">R</span></a> <a name="ConjMorph.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="ConjMorph.g"><span class="id" title="variable">g</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>) (<a name="ConjMorph.h"><span class="id" title="variable">h</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#efe2275bee4a5227161b40da886719a5"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="ConjMorph.isoG"><span class="id" title="variable">isoG</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.g"><span class="id" title="variable">g</span></a>) (<a name="ConjMorph.isoH"><span class="id" title="variable">isoH</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#isom"><span class="id" title="definition">isom</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.h"><span class="id" title="variable">h</span></a>).<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="ConjMorph.eq_hg"><span class="id" title="variable">eq_hg</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.h"><span class="id" title="variable">h</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.g"><span class="id" title="variable">g</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>) (<a name="ConjMorph.sHG"><span class="id" title="variable">sHG</span></a> : <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a>).<br/> - -<br/> -</div> - -<div class="doc"> - This does not depend on the (isoG : isom G R g) assumption. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgIsom"><span class="id" title="lemma">cfConjgIsom</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#cfIsom"><span class="id" title="definition">cfIsom</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.isoH"><span class="id" title="variable">isoH</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfIsom"><span class="id" title="definition">cfIsom</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.isoH"><span class="id" title="variable">isoH</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_isom"><span class="id" title="lemma">inertia_isom</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_R</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfIsom"><span class="id" title="definition">cfIsom</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.isoH"><span class="id" title="variable">isoH</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#70b0a61e30f130888503421fd44e1802"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph"><span class="id" title="section">ConjMorph</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ConjQuotient"><span class="id" title="section">ConjQuotient</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="ConjQuotient.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjQuotient.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgMod_norm"><span class="id" title="lemma">cfConjgMod_norm</span></a> <span class="id" title="var">H</span> <span class="id" title="var">K</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#d9227c0ae83ba0285be6deaf557252f6"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.character.classfun.html#d9227c0ae83ba0285be6deaf557252f6"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgMod"><span class="id" title="lemma">cfConjgMod</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - (<a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#d9227c0ae83ba0285be6deaf557252f6"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.character.classfun.html#d9227c0ae83ba0285be6deaf557252f6"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgQuo_norm"><span class="id" title="lemma">cfConjgQuo_norm</span></a> <span class="id" title="var">H</span> <span class="id" title="var">K</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#e2539410c9b6b2f6a5e7c9eab816ddef"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.character.classfun.html#e2539410c9b6b2f6a5e7c9eab816ddef"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgQuo"><span class="id" title="lemma">cfConjgQuo</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - (<a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#e2539410c9b6b2f6a5e7c9eab816ddef"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.character.classfun.html#e2539410c9b6b2f6a5e7c9eab816ddef"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a>)%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_mod_pre"><span class="id" title="lemma">inertia_mod_pre</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#d9227c0ae83ba0285be6deaf557252f6"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#coset"><span class="id" title="definition">coset</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#320f70d30c9a649ec82642b364681418"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_mod_quo"><span class="id" title="lemma">inertia_mod_quo</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#d9227c0ae83ba0285be6deaf557252f6"><span class="id" title="notation">%%</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a>)%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_quo"><span class="id" title="lemma">inertia_quo</span></a> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfker"><span class="id" title="definition">cfker</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">)[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#e2539410c9b6b2f6a5e7c9eab816ddef"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a>)%<span class="id" title="var">g</span>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#ConjQuotient"><span class="id" title="section">ConjQuotient</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="InertiaSdprod"><span class="id" title="section">InertiaSdprod</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="InertiaSdprod.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="InertiaSdprod.K"><span class="id" title="variable">K</span></a> <a name="InertiaSdprod.H"><span class="id" title="variable">H</span></a> <a name="InertiaSdprod.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="InertiaSdprod.defG"><span class="id" title="variable">defG</span></a> : <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.gproduct.html#4c7b411f14f1faa861c7c0ade82faf76"><span class="id" title="notation">><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.G"><span class="id" title="variable">G</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgSdprod"><span class="id" title="lemma">cfConjgSdprod</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - (<a class="idref" href="mathcomp.character.classfun.html#cfSdprod"><span class="id" title="definition">cfSdprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.defG"><span class="id" title="variable">defG</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfSdprod"><span class="id" title="definition">cfSdprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.defG"><span class="id" title="variable">defG</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>))%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_sdprod"><span class="id" title="lemma">inertia_sdprod</span></a> (<span class="id" title="var">L</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) <span class="id" title="var">phi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfSdprod"><span class="id" title="definition">cfSdprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.defG"><span class="id" title="variable">defG</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod"><span class="id" title="section">InertiaSdprod</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="InertiaDprod"><span class="id" title="section">InertiaDprod</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="InertiaDprod.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="InertiaDprod.G"><span class="id" title="variable">G</span></a> <a name="InertiaDprod.K"><span class="id" title="variable">K</span></a> <a name="InertiaDprod.H"><span class="id" title="variable">H</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">L</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> : <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.gproduct.html#191b5570f070a51bd5c860222c206828"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.gproduct.html#191b5570f070a51bd5c860222c206828"><span class="id" title="notation">x</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.G"><span class="id" title="variable">G</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgDprodl"><span class="id" title="lemma">cfConjgDprodl</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - (<a class="idref" href="mathcomp.character.classfun.html#cfDprodl"><span class="id" title="definition">cfDprodl</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfDprodl"><span class="id" title="definition">cfDprodl</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>))%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgDprodr"><span class="id" title="lemma">cfConjgDprodr</span></a> <span class="id" title="var">psi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - (<a class="idref" href="mathcomp.character.classfun.html#cfDprodr"><span class="id" title="definition">cfDprodr</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfDprodr"><span class="id" title="definition">cfDprodr</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> (<a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>))%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgDprod"><span class="id" title="lemma">cfConjgDprod</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - (<a class="idref" href="mathcomp.character.classfun.html#cfDprod"><span class="id" title="definition">cfDprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfDprod"><span class="id" title="definition">cfDprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a>))%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_dprodl"><span class="id" title="lemma">inertia_dprodl</span></a> <span class="id" title="var">L</span> <span class="id" title="var">phi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfDprodl"><span class="id" title="definition">cfDprodl</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_dprodr"><span class="id" title="lemma">inertia_dprodr</span></a> <span class="id" title="var">L</span> <span class="id" title="var">psi</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfDprodr"><span class="id" title="definition">cfDprodr</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_dprod"><span class="id" title="lemma">inertia_dprod</span></a> <span class="id" title="var">L</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<span class="id" title="var">psi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> 1%<span class="id" title="var">g</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> 1%<span class="id" title="var">g</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <br/> - <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfDprod"><span class="id" title="definition">cfDprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_dprod_irr"><span class="id" title="lemma">inertia_dprod_irr</span></a> <span class="id" title="var">L</span> <span class="id" title="var">i</span> <span class="id" title="var">j</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfDprod"><span class="id" title="definition">cfDprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.KxH"><span class="id" title="variable">KxH</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod"><span class="id" title="section">InertiaDprod</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="InertiaBigdprod"><span class="id" title="section">InertiaBigdprod</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="InertiaBigdprod.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="InertiaBigdprod.P"><span class="id" title="variable">P</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.character.inertia.html#I"><span class="id" title="variable">I</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="InertiaBigdprod.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="InertiaBigdprod.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">L</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.fingroup.gproduct.html#dprod"><span class="id" title="abbreviation">dprod</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">g</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.G"><span class="id" title="variable">G</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="InertiaBigdprod.ConjBig"><span class="id" title="section">ConjBig</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="InertiaBigdprod.ConjBig.y"><span class="id" title="variable">y</span></a> : <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a>.<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="InertiaBigdprod.ConjBig.nAy"><span class="id" title="variable">nAy</span></a>: <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.ConjBig.y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgBigdprodi"><span class="id" title="lemma">cfConjgBigdprodi</span></a> <span class="id" title="var">i</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - (<a class="idref" href="mathcomp.character.classfun.html#cfBigdprodi"><span class="id" title="definition">cfBigdprodi</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.ConjBig.y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfBigdprodi"><span class="id" title="definition">cfBigdprodi</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.ConjBig.y"><span class="id" title="variable">y</span></a>))%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cfConjgBigdprod"><span class="id" title="lemma">cfConjgBigdprod</span></a> <span class="id" title="var">phi</span> :<br/> - (<a class="idref" href="mathcomp.character.classfun.html#cfBigdprod"><span class="id" title="definition">cfBigdprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.ConjBig.y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfBigdprod"><span class="id" title="definition">cfBigdprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> ⇒ <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#f5adf0d90696e8392e1d3055eb6479b6"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.ConjBig.y"><span class="id" title="variable">y</span></a>))%<span class="id" title="var">CF</span>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.ConjBig"><span class="id" title="section">ConjBig</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="InertiaBigdprod.InertiaBig"><span class="id" title="section">InertiaBig</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="InertiaBigdprod.InertiaBig.L"><span class="id" title="variable">L</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="InertiaBigdprod.InertiaBig.nAL"><span class="id" title="variable">nAL</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.InertiaBig.L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_bigdprodi"><span class="id" title="lemma">inertia_bigdprodi</span></a> <span class="id" title="var">i</span> (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfBigdprodi"><span class="id" title="definition">cfBigdprodi</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_bigdprod"><span class="id" title="lemma">inertia_bigdprod</span></a> <span class="id" title="var">phi</span> (<span class="id" title="var">Phi</span> := <a class="idref" href="mathcomp.character.classfun.html#cfBigdprod"><span class="id" title="definition">cfBigdprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#Phi"><span class="id" title="variable">Phi</span></a> 1%<span class="id" title="var">g</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Phi"><span class="id" title="variable">Phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.InertiaBig.L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="inertia_bigdprod_irr"><span class="id" title="lemma">inertia_bigdprod_irr</span></a> <span class="id" title="var">Iphi</span> (<span class="id" title="var">phi</span> := <span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> ⇒ <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Iphi"><span class="id" title="variable">Iphi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#cfBigdprod"><span class="id" title="definition">cfBigdprod</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.InertiaBig.L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.InertiaBig"><span class="id" title="section">InertiaBig</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod"><span class="id" title="section">InertiaBigdprod</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ConsttInertiaBijection"><span class="id" title="section">ConsttInertiaBijection</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ConsttInertiaBijection.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="ConsttInertiaBijection.H"><span class="id" title="variable">H</span></a> <a name="ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="ConsttInertiaBijection.t"><span class="id" title="variable">t</span></a> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a>).<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="ConsttInertiaBijection.nsHG"><span class="id" title="variable">nsHG</span></a> : <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a> := <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#T"><span class="id" title="abbreviation">T</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="abbreviation">theta</span></a>).<br/> -<span class="id" title="keyword">Let</span> <a name="ConsttInertiaBijection.calB"><span class="id" title="variable">calB</span></a> := <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="abbreviation">theta</span></a>).<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem (6.11). -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="constt_Inertia_bijection"><span class="id" title="lemma">constt_Inertia_bijection</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b76985613d3b3ca583bb3217c76109bb"><span class="id" title="notation">[/\</span></a> <span class="comment">(*a*)</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">s</span>, <a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_s</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b76985613d3b3ca583bb3217c76109bb"><span class="id" title="notation">,</span></a><br/> - <span class="comment">(*b*)</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> (<a class="idref" href="mathcomp.character.character.html#Ind_Iirr"><span class="id" title="definition">Ind_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b76985613d3b3ca583bb3217c76109bb"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="mathcomp.character.character.html#Ind_Iirr"><span class="id" title="definition">Ind_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calB"><span class="id" title="variable">calB</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b76985613d3b3ca583bb3217c76109bb"><span class="id" title="notation">,</span></a><br/> - <span class="comment">(*c*)</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">s</span> (<span class="id" title="var">psi</span> := <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_s</span></a>) (<span class="id" title="var">chi</span> := <a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a>),<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9505898acdd70a74fca20676bf8d8084"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9505898acdd70a74fca20676bf8d8084"><span class="id" title="notation">predI</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9505898acdd70a74fca20676bf8d8084"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9505898acdd70a74fca20676bf8d8084"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#pred1"><span class="id" title="definition">pred1</span></a> <a class="idref" href="mathcomp.character.inertia.html#s"><span class="id" title="variable">s</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b76985613d3b3ca583bb3217c76109bb"><span class="id" title="notation">&</span></a> <span class="comment">(*d*)</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">s</span> (<span class="id" title="var">psi</span> := <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_s</span></a>) (<span class="id" title="var">chi</span> := <a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a>),<br/> - <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">psi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="abbreviation">theta</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="abbreviation">theta</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b76985613d3b3ca583bb3217c76109bb"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection"><span class="id" title="section">ConsttInertiaBijection</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ExtendInvariantIrr"><span class="id" title="section">ExtendInvariantIrr</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="ExtendInvariantIrr.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">G</span> <span class="id" title="var">H</span> <span class="id" title="var">K</span> <span class="id" title="var">L</span> <span class="id" title="var">M</span> <span class="id" title="var">N</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ExtendInvariantIrr.ConsttIndExtendible"><span class="id" title="section">ConsttIndExtendible</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a> <a name="ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="ExtendInvariantIrr.ConsttIndExtendible.t"><span class="id" title="variable">t</span></a> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a>) (<a name="ExtendInvariantIrr.ConsttIndExtendible.c"><span class="id" title="variable">c</span></a> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a>).<br/> -<span class="id" title="keyword">Let</span> <a name="ExtendInvariantIrr.ConsttIndExtendible.theta"><span class="id" title="variable">theta</span></a> := <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_t</span></a>.<br/> -<span class="id" title="keyword">Let</span> <a name="ExtendInvariantIrr.ConsttIndExtendible.chi"><span class="id" title="variable">chi</span></a> := <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_c</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="mul_Iirr"><span class="id" title="definition">mul_Iirr</span></a> <span class="id" title="var">b</span> := <a class="idref" href="mathcomp.character.character.html#cfIirr"><span class="id" title="definition">cfIirr</span></a> (<a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_b</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.chi"><span class="id" title="variable">chi</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="mul_mod_Iirr"><span class="id" title="definition">mul_mod_Iirr</span></a> (<span class="id" title="var">b</span> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> (<a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a>)) := <a class="idref" href="mathcomp.character.inertia.html#mul_Iirr"><span class="id" title="definition">mul_Iirr</span></a> (<a class="idref" href="mathcomp.character.character.html#mod_Iirr"><span class="id" title="definition">mod_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#b"><span class="id" title="variable">b</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="ExtendInvariantIrr.ConsttIndExtendible.nsNG"><span class="id" title="variable">nsNG</span></a> : <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a>) (<a name="ExtendInvariantIrr.ConsttIndExtendible.cNt"><span class="id" title="variable">cNt</span></a> : <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.theta"><span class="id" title="variable">theta</span></a>).<br/> -<span class="id" title="keyword">Let</span> <a name="ExtendInvariantIrr.ConsttIndExtendible.sNG"><span class="id" title="variable">sNG</span></a> : <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a>. <br/> -<span class="id" title="keyword">Let</span> <a name="ExtendInvariantIrr.ConsttIndExtendible.nNG"><span class="id" title="variable">nNG</span></a> : <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#1ff9e060a8cc6098d64e42214fa57c96"><span class="id" title="notation">)</span></a>. <br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="extendible_irr_invariant"><span class="id" title="lemma">extendible_irr_invariant</span></a> : <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Let</span> <a name="ExtendInvariantIrr.ConsttIndExtendible.IGtheta"><span class="id" title="variable">IGtheta</span></a> := <a class="idref" href="mathcomp.character.inertia.html#extendible_irr_invariant"><span class="id" title="lemma">extendible_irr_invariant</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem (6.16) -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="constt_Ind_mul_ext"><span class="id" title="lemma">constt_Ind_mul_ext</span></a> <span class="id" title="var">f</span> (<span class="id" title="var">phi</span> := <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_f</span></a>) (<span class="id" title="var">psi</span> := <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.theta"><span class="id" title="variable">theta</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">calS</span> := <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">phi</span></a>) <span class="id" title="tactic">in</span><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">[/\</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#calS"><span class="id" title="variable">calS</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">b</span>, <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_b</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#calS"><span class="id" title="variable">calS</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#mul_Iirr"><span class="id" title="definition">mul_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">psi</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.character.inertia.html#mul_Iirr"><span class="id" title="definition">mul_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">b</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#calS"><span class="id" title="variable">calS</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">]</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#calS"><span class="id" title="variable">calS</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_b</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#mul_Iirr"><span class="id" title="definition">mul_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Corollary (6.17) (due to Gallagher). -</div> -<div class="code"> -<span class="id" title="keyword">Corollary</span> <a name="constt_Ind_ext"><span class="id" title="lemma">constt_Ind_ext</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">[/\</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> (<a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a>), <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#mod_Iirr"><span class="id" title="definition">mod_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#mul_mod_Iirr"><span class="id" title="definition">mul_mod_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">theta</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#codom"><span class="id" title="definition">codom</span></a> <a class="idref" href="mathcomp.character.inertia.html#mul_mod_Iirr"><span class="id" title="definition">mul_mod_Iirr</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#523c64af6ca44fabb3f80902002d2d06"><span class="id" title="notation">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#de3e30c288f66ee879ea2b40e81e186c"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#de3e30c288f66ee879ea2b40e81e186c"><span class="id" title="notation">sum_b</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_b</span></a> 1%<span class="id" title="var">g</span> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#mul_mod_Iirr"><span class="id" title="definition">mul_mod_Iirr</span></a> <a class="idref" href="mathcomp.character.inertia.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#554fc3f3cf0a27fe0863b7741d119014"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible"><span class="id" title="section">ConsttIndExtendible</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem (6.19). -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="invariant_chief_irr_cases"><span class="id" title="lemma">invariant_chief_irr_cases</span></a> <span class="id" title="var">G</span> <span class="id" title="var">K</span> <span class="id" title="var">L</span> <span class="id" title="var">s</span> (<span class="id" title="var">theta</span> := <a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_s</span></a>) :<br/> - <a class="idref" href="mathcomp.solvable.gseries.html#chief_factor"><span class="id" title="definition">chief_factor</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> (<a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">t</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#695cfe96d0d877b42f665707f55629d3"><span class="id" title="notation">[\/</span></a> <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#695cfe96d0d877b42f665707f55629d3"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">e</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">p</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#e"><span class="id" title="variable">e</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> (<a class="idref" href="mathcomp.character.inertia.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">^</span></a> 2)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#t"><span class="id" title="variable">t</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#695cfe96d0d877b42f665707f55629d3"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">p</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.character.inertia.html#t"><span class="id" title="variable">t</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#695cfe96d0d877b42f665707f55629d3"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Corollary (6.19). -</div> -<div class="code"> -<span class="id" title="keyword">Corollary</span> <a name="cfRes_prime_irr_cases"><span class="id" title="lemma">cfRes_prime_irr_cases</span></a> <span class="id" title="var">G</span> <span class="id" title="var">N</span> <span class="id" title="var">s</span> <span class="id" title="var">p</span> (<span class="id" title="var">chi</span> := <a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_s</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.prime.html#prime"><span class="id" title="definition">prime</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#3d89e510dca4cdafae52010baf4f7636"><span class="id" title="notation">[\/</span></a> <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#3d89e510dca4cdafae52010baf4f7636"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">c</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#c"><span class="id" title="variable">c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#c"><span class="id" title="variable">c</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#3d89e510dca4cdafae52010baf4f7636"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Corollary (6.20). -</div> -<div class="code"> -<span class="id" title="keyword">Corollary</span> <a name="prime_invariant_irr_extendible"><span class="id" title="lemma">prime_invariant_irr_extendible</span></a> <span class="id" title="var">G</span> <span class="id" title="var">N</span> <span class="id" title="var">s</span> <span class="id" title="var">p</span> :<br/> - <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.prime.html#prime"><span class="id" title="definition">prime</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_s</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">{</span></a><span class="id" title="var">t</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_t</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_s</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Lemma (6.24). -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="extend_to_cfdet"><span class="id" title="lemma">extend_to_cfdet</span></a> <span class="id" title="var">G</span> <span class="id" title="var">N</span> <span class="id" title="var">s</span> <span class="id" title="var">c0</span> <span class="id" title="var">u</span> :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">theta</span> := <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_s</span></a> <span class="id" title="tactic">in</span> <span class="id" title="keyword">let</span> <span class="id" title="var">lambda</span> := <a class="idref" href="mathcomp.character.character.html#cfDet"><span class="id" title="definition">cfDet</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <span class="id" title="tactic">in</span> <span class="id" title="keyword">let</span> <span class="id" title="var">mu</span> := <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_u</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> (<a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.truncC"><span class="id" title="definition">truncC</span></a> (<a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> 1%<span class="id" title="var">g</span>)) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_c0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.inertia.html#mu"><span class="id" title="variable">mu</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">c</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi_c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.character.character.html#cfDet"><span class="id" title="definition">cfDet</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#mu"><span class="id" title="variable">mu</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">c1</span>, <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi_c1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.character.html#cfDet"><span class="id" title="definition">cfDet</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_c1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#mu"><span class="id" title="variable">mu</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#c1"><span class="id" title="variable">c1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#c"><span class="id" title="variable">c</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem (6.25). -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="solvable_irr_extendible_from_det"><span class="id" title="lemma">solvable_irr_extendible_from_det</span></a> <span class="id" title="var">G</span> <span class="id" title="var">N</span> <span class="id" title="var">s</span> (<span class="id" title="var">theta</span> := <a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_s</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.nilpotent.html#solvable"><span class="id" title="definition">solvable</span></a> (<a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> (<a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.truncC"><span class="id" title="definition">truncC</span></a> (<a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> 1%<span class="id" title="var">g</span>)) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <br/> - <a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">∃</span></a> <span class="id" title="var">c</span><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">_c</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">]</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">_u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.character.character.html#cfDet"><span class="id" title="definition">cfDet</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem (6.26). -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="extend_linear_char_from_Sylow"><span class="id" title="lemma">extend_linear_char_from_Sylow</span></a> <span class="id" title="var">G</span> <span class="id" title="var">N</span> (<span class="id" title="var">lambda</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#linear_char"><span class="id" title="definition">linear_char</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">p</span>, <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">pi</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span><a class="idref" href="mathcomp.ssreflect.prime.html#c36dd927e8fe3f2052f45795266a50d2"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">Hp</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">,</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Hp"><span class="id" title="variable">Hp</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#Hp"><span class="id" title="variable">Hp</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#081d3e80d093e95dd63e6bafc24fef78"><span class="id" title="notation">)</span></a> (<a class="idref" href="mathcomp.character.inertia.html#Hp"><span class="id" title="variable">Hp</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a>)%<span class="id" title="var">g</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">]</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#59ba2b47d2814e66f8210a649ae6e6bc"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Hp</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">_u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5dde21e605844589296bf0aeffd7b476"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Corollary (6.27). -</div> -<div class="code"> -<span class="id" title="keyword">Corollary</span> <a name="extend_coprime_linear_char"><span class="id" title="lemma">extend_coprime_linear_char</span></a> <span class="id" title="var">G</span> <span class="id" title="var">N</span> (<span class="id" title="var">lambda</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#linear_char"><span class="id" title="definition">linear_char</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">_u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_u</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">v</span>,<br/> - <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi_v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#lambda"><span class="id" title="variable">lambda</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_v</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.inertia.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Corollary (6.28). -</div> -<div class="code"> -<span class="id" title="keyword">Corollary</span> <a name="extend_solvable_coprime_irr"><span class="id" title="lemma">extend_solvable_coprime_irr</span></a> <span class="id" title="var">G</span> <span class="id" title="var">N</span> <span class="id" title="var">t</span> (<span class="id" title="var">theta</span> := <a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_t</span></a>) :<br/> - <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7e8095b432e7aa5c3c22bb87584658b7"><span class="id" title="notation"><|</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.nilpotent.html#solvable"><span class="id" title="definition">solvable</span></a> (<a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#3e65ad3edf5f7fb3ea6bc63a878112a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.character.inertia.html#36dd32662053dbe9e0b1392d97fc5421"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> (<a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.truncC"><span class="id" title="definition">truncC</span></a> (<a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> 1%<span class="id" title="var">g</span>)) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">c</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">_c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_c</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">d</span>,<br/> - <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#06cfee1f9bee2f85a584c7483fb59a63"><span class="id" title="notation">chi_d</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#0665f11b64f1431f9d664aba3c000866"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_d</span></a><a class="idref" href="mathcomp.character.character.html#8adcf036f3cd1d43410cc3f8faabe076"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.character.inertia.html#d"><span class="id" title="variable">d</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#c"><span class="id" title="variable">c</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr"><span class="id" title="section">ExtendInvariantIrr</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Frobenius"><span class="id" title="section">Frobenius</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Frobenius.gT"><span class="id" title="variable">gT</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<a name="Frobenius.G"><span class="id" title="variable">G</span></a> <a name="Frobenius.K"><span class="id" title="variable">K</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -</div> - -<div class="doc"> - Because he only defines Frobenius groups in chapter 7, Isaacs does not - state these theorems using the Frobenius property. -</div> -<div class="code"> -<span class="id" title="keyword">Hypothesis</span> <a name="Frobenius.frobGK"><span class="id" title="variable">frobGK</span></a> : <a class="idref" href="mathcomp.solvable.frobenius.html#74eaff00fb742dcd0d78d509b2b0e3f8"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#74eaff00fb742dcd0d78d509b2b0e3f8"><span class="id" title="notation">Frobenius</span></a> <a class="idref" href="mathcomp.character.inertia.html#Frobenius.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#74eaff00fb742dcd0d78d509b2b0e3f8"><span class="id" title="notation">with</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#74eaff00fb742dcd0d78d509b2b0e3f8"><span class="id" title="notation">kernel</span></a> <a class="idref" href="mathcomp.character.inertia.html#Frobenius.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#74eaff00fb742dcd0d78d509b2b0e3f8"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem 6.34(a1). -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="inertia_Frobenius_ker"><span class="id" title="lemma">inertia_Frobenius_ker</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Frobenius.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a><a class="idref" href="mathcomp.character.inertia.html#29a4a6551768a30e0931d50967fa7f19"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#Frobenius.K"><span class="id" title="variable">K</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem 6.34(a2) -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="irr_induced_Frobenius_ker"><span class="id" title="lemma">irr_induced_Frobenius_ker</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Frobenius.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#Frobenius.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.inertia.html#Frobenius.G"><span class="id" title="variable">G</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - This is Isaacs, Theorem 6.34(b) -</div> -<div class="code"> -<span class="id" title="keyword">Theorem</span> <a name="Frobenius_Ind_irrP"><span class="id" title="lemma">Frobenius_Ind_irrP</span></a> <span class="id" title="var">j</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">i</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.inertia.html#Frobenius.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#Frobenius.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.character.classfun.html#c8e0ccc285497008e15e1f92f34d54bd"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a>)<br/> - (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Frobenius.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfker"><span class="id" title="definition">cfker</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">)</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.inertia.html#Frobenius"><span class="id" title="section">Frobenius</span></a>.<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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