generate the documentation for 1.7

author: Enrico Tassi 2018-04-20 10:54:22 +0200
committer: Enrico Tassi 2018-04-20 10:54:22 +0200
commit: ed05182cece6bb3706e09b2ce14af4a41a2e8141 (patch)
tree: e850d7314b6372d0476cf2ffaf7d3830721db7b1 /docs/htmldoc/mathcomp.character.inertia.html
parent: 3d196f44681fb3b23ff8a79fbd44e12308680531 (diff)
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+<title>mathcomp.character.inertia</title>
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+<div id="page">
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+</div>
+
+<div id="main">
+
+<h1 class="libtitle">Library mathcomp.character.inertia</h1>
+
+<div class="code">
+<span class="comment">(*&nbsp;(c)&nbsp;Copyright&nbsp;2006-2016&nbsp;Microsoft&nbsp;Corporation&nbsp;and&nbsp;Inria.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br/>
+&nbsp;Distributed&nbsp;under&nbsp;the&nbsp;terms&nbsp;of&nbsp;CeCILL-B.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*)</span><br/>
+<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="mathcomp.ssreflect.ssreflect.html#"><span class="id" title="library">mathcomp.ssreflect.ssreflect</span></a>.<br/>
+
+<br/>
+<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 :&amp;: '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> &quot;''I[' phi ]"<br/>
+&nbsp;&nbsp;(<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> &quot;''I_' G [ phi ]"<br/>
+&nbsp;&nbsp;(<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#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/>
+&nbsp;&nbsp;<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#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><span class="id" title="notation">ffun</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><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/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="abbreviation">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><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#808c6b8e35e792f23899f360a21e4638"><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#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.character.inertia.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="mathcomp.ssreflect.finfun.html#71fbd02a8ba525d8dcd88d59800c905e"><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="c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">&quot;</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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/>
+<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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#808c6b8e35e792f23899f360a21e4638"><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#a605acbeae7597f74f5a9b816ed8a717"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#808c6b8e35e792f23899f360a21e4638"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;(<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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#169fb610eeaa28cebf8ec36928167473"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#169fb610eeaa28cebf8ec36928167473"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">^</span></a> 1)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.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/8.8.0/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#a605acbeae7597f74f5a9b816ed8a717"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/8.8.0/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#a605acbeae7597f74f5a9b816ed8a717"><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/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">_A</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><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#1deb3845cf16de446ae6619879e9d6db"><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#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">_A</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">'1</span></a><a class="idref" href="mathcomp.character.classfun.html#81548e24b43b8ac2b7016bb7670121ae"><span class="id" title="notation">_A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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#8900f6ae77a86586561e15965d5870c7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8900f6ae77a86586561e15965d5870c7"><span class="id" title="notation">lrmorphism</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8900f6ae77a86586561e15965d5870c7"><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#8900f6ae77a86586561e15965d5870c7"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#9c355fdbf8ab6d681afb9e674f9c39c9"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#9c355fdbf8ab6d681afb9e674f9c39c9"><span class="id" title="notation">)^*</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#9c355fdbf8ab6d681afb9e674f9c39c9"><span class="id" title="notation">^*</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Conj.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#1deb3845cf16de446ae6619879e9d6db"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :=  <br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#11a9aebd9632a5968df4f5811663355a"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#17d28d004d0863cb022d4ce832ddaaae"><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#11a9aebd9632a5968df4f5811663355a"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) <span class="id" title="var">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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/>
+<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.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#808c6b8e35e792f23899f360a21e4638"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</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#c43b3c1da4b45406b21f77f06bf1131e"><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#17d28d004d0863cb022d4ce832ddaaae"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#291276ea06db0b00a2747a79d012bbe0"><span class="id" title="notation">:*</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/>
+
+<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#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><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#507fd39a15bb9cb7e52e1aaa9e2285b5"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#507fd39a15bb9cb7e52e1aaa9e2285b5"><span class="id" title="notation">C_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#507fd39a15bb9cb7e52e1aaa9e2285b5"><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#507fd39a15bb9cb7e52e1aaa9e2285b5"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.solvable.center.html#07d637974acf808c1caadc3b5bdfa6d3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.solvable.center.html#07d637974acf808c1caadc3b5bdfa6d3"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.solvable.center.html#07d637974acf808c1caadc3b5bdfa6d3"><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#07d637974acf808c1caadc3b5bdfa6d3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#1deb3845cf16de446ae6619879e9d6db"><span class="id" title="notation">:^</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">[</span></a>0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#ae4d81913e6239182a9ac7467ffde8cd"><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#99fa4ab272515ca96008d1110d766674"><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/8.8.0/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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">&lt;-</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#7c55545b71d81bfa21b7c36ce13dfa39"><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#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#cbc2f2ab11c1c376b5c4511d28b14d74"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#cbc2f2ab11c1c376b5c4511d28b14d74"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#cbc2f2ab11c1c376b5c4511d28b14d74"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#cbc2f2ab11c1c376b5c4511d28b14d74"><span class="id" title="notation">&lt;-</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#cbc2f2ab11c1c376b5c4511d28b14d74"><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#cbc2f2ab11c1c376b5c4511d28b14d74"><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#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#81f8078534dcbb7e13a32d292f766525"><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#99fa4ab272515ca96008d1110d766674"><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#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#81f8078534dcbb7e13a32d292f766525"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">[</span></a>1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">[</span></a>1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#22058a36a53dac65c94ca403bc62650a"><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#99fa4ab272515ca96008d1110d766674"><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/8.8.0/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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">&lt;-</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#7c55545b71d81bfa21b7c36ce13dfa39"><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#7c55545b71d81bfa21b7c36ce13dfa39"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#358fca18835530a08faf9e0f246b584a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#358fca18835530a08faf9e0f246b584a"><span class="id" title="notation">prod_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#358fca18835530a08faf9e0f246b584a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#358fca18835530a08faf9e0f246b584a"><span class="id" title="notation">&lt;-</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#358fca18835530a08faf9e0f246b584a"><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#358fca18835530a08faf9e0f246b584a"><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#99fa4ab272515ca96008d1110d766674"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#chi"><span class="id" title="variable">chi</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/>
+
+<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/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><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#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_i</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">C</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#67c26168baa7671aab03da2a0fb7dafa"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_0</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<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/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><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/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#101f65e74897bbc2c1bee8f833b19e33"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><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#101f65e74897bbc2c1bee8f833b19e33"><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#101f65e74897bbc2c1bee8f833b19e33"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/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/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><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/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><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#a605acbeae7597f74f5a9b816ed8a717"><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/8.8.0/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/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><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#a605acbeae7597f74f5a9b816ed8a717"><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/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><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/8.8.0/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/8.8.0/stdlib//Coq.ssr.ssrfun.html#8f28bbd804547edd8de802d63ef85617"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#7f8443d955f2fbb3e80ccc8bc17d3b2e"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#7f8443d955f2fbb3e80ccc8bc17d3b2e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#7f8443d955f2fbb3e80ccc8bc17d3b2e"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#7f8443d955f2fbb3e80ccc8bc17d3b2e"><span class="id" title="notation">_H</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">)%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><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#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) := <br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">|</span></a> <span class="id" title="var">Tx</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><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#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_B</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><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#6a989a6414a722580f13fcad5931885d"><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#fb029fd23b6fc39e014fe7658d797041"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">y</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&amp;</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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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#ddda694c2b3215cd89e224821b0146f2"><span class="id" title="notation">^:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">N_G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#7193b23d12b4f3c2146b0e77ee974b2b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/>
+&nbsp;&nbsp;(<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#ddda694c2b3215cd89e224821b0146f2"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (1 <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#36229928b54642a4a7da943ccf8f9612"><span class="id" title="notation">[::</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#36229928b54642a4a7da943ccf8f9612"><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#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) <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#f2bdcb40cf423bf8d54f091f6cec6964"><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/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#17d28d004d0863cb022d4ce832ddaaae"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="im_cfclass_Iirr"><span class="id" title="lemma">im_cfclass_Iirr</span></a> <span class="id" title="var">i</span> :<br/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">|</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><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#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">]</span></a> (<a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.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#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#6a989a6414a722580f13fcad5931885d"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">i</span> :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.bigop.html#30705c25db0a97e8b1b08168f9199b27"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#30705c25db0a97e8b1b08168f9199b27"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#30705c25db0a97e8b1b08168f9199b27"><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#30705c25db0a97e8b1b08168f9199b27"><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#30705c25db0a97e8b1b08168f9199b27"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#30705c25db0a97e8b1b08168f9199b27"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#30705c25db0a97e8b1b08168f9199b27"><span class="id" title="notation">(</span></a><span class="id" title="var">chi</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#30705c25db0a97e8b1b08168f9199b27"><span class="id" title="notation">&lt;-</span></a> (<a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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#30705c25db0a97e8b1b08168f9199b27"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><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#8850ee6edf9a388b1213678f3d3ee856"><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#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> (<a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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#8850ee6edf9a388b1213678f3d3ee856"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">]</span></a> (<a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">R</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#f3016d4e55aa553d3e912592ec65e342"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">(</span></a><span class="id" title="var">y</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><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#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">(</span></a><span class="id" title="var">chi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">&lt;-</span></a> (<a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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#c9afba1af653123a1dddfe925d2b3ab3"><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#81f8078534dcbb7e13a32d292f766525"><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/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#99fa4ab272515ca96008d1110d766674"><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#99fa4ab272515ca96008d1110d766674"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">('</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">H</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">psi</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#Inertia.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><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/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#Inertia.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfker"><span class="id" title="definition">cfker</span></a> <a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> (<a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">n</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> (<a class="idref" href="mathcomp.character.inertia.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.inertia.html#ddda694c2b3215cd89e224821b0146f2"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><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="454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">&quot;</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="bbf8bdfd5eeac2938107d0cd6fd21df9"><span class="id" title="notation">&quot;</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="0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">&quot;</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#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">[</span></a><span class="id" title="var">phi</span><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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="9298a88c2737a890cdd39d39e1c88c67"><span class="id" title="notation">&quot;</span></a>''I_' G [ phi ] " := (<span class="id" title="var">G</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#afecdac1581fada66d09c1ab40cfc23e"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.character.inertia.html#bbf8bdfd5eeac2938107d0cd6fd21df9"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#bbf8bdfd5eeac2938107d0cd6fd21df9"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#bbf8bdfd5eeac2938107d0cd6fd21df9"><span class="id" title="notation">[</span></a><span class="id" title="var">phi</span><a class="idref" href="mathcomp.character.inertia.html#bbf8bdfd5eeac2938107d0cd6fd21df9"><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="0caf5e3293e9c551b3271b02f0fdad55"><span class="id" title="notation">&quot;</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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/>
+
+<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/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><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/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><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/>
+&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#0e30e69542492ea333fdb332a7a36e8f"><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/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><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/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">phi</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">y</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">)%</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><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/>
+&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjRestrict.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#0e30e69542492ea333fdb332a7a36e8f"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_T</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.character.inertia.html#0caf5e3293e9c551b3271b02f0fdad55"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#36229928b54642a4a7da943ccf8f9612"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#36229928b54642a4a7da943ccf8f9612"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="ConjMorph.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.character.inertia.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">&gt;-&gt;</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#c5b2825fcd994c4c5cc69df8802f5376"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#48cff845c81518398138031392d44c93"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#48cff845c81518398138031392d44c93"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</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#619a2190d60a66179f3396458e2a09ae"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#48cff845c81518398138031392d44c93"><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#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#48cff845c81518398138031392d44c93"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#48cff845c81518398138031392d44c93"><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#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/>
+<span class="id" title="keyword">Variables</span> (<a name="ConjMorph.g"><span class="id" title="variable">g</span></a> : <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><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#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">&gt;-&gt;</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#c5b2825fcd994c4c5cc69df8802f5376"><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#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">morphism</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#c5b2825fcd994c4c5cc69df8802f5376"><span class="id" title="notation">&gt;-&gt;</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#c5b2825fcd994c4c5cc69df8802f5376"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.h"><span class="id" title="variable">h</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.g"><span class="id" title="variable">g</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>) (<a 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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.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/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ConjMorph.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_R</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjMorph.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.fingroup.morphism.html#48cff845c81518398138031392d44c93"><span class="id" title="notation">@*</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConjQuotient.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/>
+
+<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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#c7768147d2d560601601fbf95706ddcc"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#a2eb54061d3ca3afb342283ba33dfae2"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#a2eb54061d3ca3afb342283ba33dfae2"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#c7768147d2d560601601fbf95706ddcc"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;(<a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#a2eb54061d3ca3afb342283ba33dfae2"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#a2eb54061d3ca3afb342283ba33dfae2"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#db52ff60a779407895b2e9da59342e63"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#db52ff60a779407895b2e9da59342e63"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;(<a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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#db52ff60a779407895b2e9da59342e63"><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#c43b3c1da4b45406b21f77f06bf1131e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#db52ff60a779407895b2e9da59342e63"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#c7768147d2d560601601fbf95706ddcc"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#a2eb54061d3ca3afb342283ba33dfae2"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</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#619a2190d60a66179f3396458e2a09ae"><span class="id" title="notation">@*^-1</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#c7768147d2d560601601fbf95706ddcc"><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#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#c7768147d2d560601601fbf95706ddcc"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#a2eb54061d3ca3afb342283ba33dfae2"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#c7768147d2d560601601fbf95706ddcc"><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#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#c7768147d2d560601601fbf95706ddcc"><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#0e30e69542492ea333fdb332a7a36e8f"><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#db52ff60a779407895b2e9da59342e63"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> (<a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.fingroup.quotient.html#c7768147d2d560601601fbf95706ddcc"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/>
+
+<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#ff5a974c523b8d4c8927273818a26a02"><span class="id" title="notation">&gt;&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;(<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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) <span class="id" title="var">phi</span> :<br/>
+&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaSdprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/>
+<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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/>
+<span class="id" title="keyword">Hypothesis</span> <a name="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#3733c0e43956ad2062ab5f1e57ceb9a8"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.fingroup.gproduct.html#3733c0e43956ad2062ab5f1e57ceb9a8"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;(<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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;(<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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;(<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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/>
+&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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/>
+&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) (<span class="id" title="var">psi</span> : <a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.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#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.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#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.K"><span class="id" title="variable">K</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#InertiaDprod.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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/8.8.0/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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="InertiaBigdprod.G"><span class="id" title="variable">G</span></a> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/>
+<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">L</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/>
+<span class="id" title="keyword">Hypothesis</span> <a name="InertiaBigdprod.defG"><span class="id" title="variable">defG</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><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#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">g</span><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#8850ee6edf9a388b1213678f3d3ee856"><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#8850ee6edf9a388b1213678f3d3ee856"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.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#3cae19671031307d430e5b14ccbd1058"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;(<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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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/>
+&nbsp;&nbsp;(<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#c43b3c1da4b45406b21f77f06bf1131e"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#c43b3c1da4b45406b21f77f06bf1131e"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/>
+<span class="id" title="keyword">Hypothesis</span> <a name="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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.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#3cae19671031307d430e5b14ccbd1058"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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/>
+&nbsp;&nbsp;<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#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.InertiaBig.L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><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#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#InertiaBigdprod.InertiaBig.L"><span class="id" title="variable">L</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&amp;:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1875f5a227b27f2ac759a0935c29c8e2"><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#1875f5a227b27f2ac759a0935c29c8e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_L</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><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#0e30e69542492ea333fdb332a7a36e8f"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><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/>
+&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#c7fe7fb0f694e91a7e258ff78a0390ef"><span class="id" title="notation">[/\</span></a> <span class="comment">(*a*)</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">s</span>, <a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_s</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#c7fe7fb0f694e91a7e258ff78a0390ef"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="comment">(*b*)</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> (<a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#c7fe7fb0f694e91a7e258ff78a0390ef"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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#f2bdcb40cf423bf8d54f091f6cec6964"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calB"><span class="id" title="variable">calB</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#c7fe7fb0f694e91a7e258ff78a0390ef"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="comment">(*c*)</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">s</span> (<span class="id" title="var">psi</span> := <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_s</span></a>) (<span class="id" title="var">chi</span> := <a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#bc8da799462dbe647b502e63c7d6c405"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#bc8da799462dbe647b502e63c7d6c405"><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#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#bc8da799462dbe647b502e63c7d6c405"><span class="id" title="notation">&amp;</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/8.8.0/stdlib//Coq.ssr.ssrbool.html#bc8da799462dbe647b502e63c7d6c405"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a><br/>
+&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#c7fe7fb0f694e91a7e258ff78a0390ef"><span class="id" title="notation">&amp;</span></a> <span class="comment">(*d*)</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#ConsttInertiaBijection.calA"><span class="id" title="variable">calA</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">s</span> (<span class="id" title="var">psi</span> := <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_s</span></a>) (<span class="id" title="var">chi</span> := <a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#7e29b86b76573eecf4b9c8a0ccdb9715"><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#7e29b86b76573eecf4b9c8a0ccdb9715"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">psi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><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#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><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#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#c7fe7fb0f694e91a7e258ff78a0390ef"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>.<br/>
+
+<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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>) (<a name="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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_b</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><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#c7768147d2d560601601fbf95706ddcc"><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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.ConsttIndExtendible.N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#3cae19671031307d430e5b14ccbd1058"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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#454089fa36b980e0a936e7f532a99179"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#22058a36a53dac65c94ca403bc62650a"><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/>
+&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<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#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">phi</span></a>) <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">[/\</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#calS"><span class="id" title="variable">calS</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">b</span>, <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_b</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.inertia.html#calS"><span class="id" title="variable">calS</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#mul_Iirr"><span class="id" title="definition">mul_Iirr</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">psi</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><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#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">|</span></a> <span class="id" title="var">b</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><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#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">]</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><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#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_b</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">]</span></a>.<br/>
+
+<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/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">[/\</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">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#c7768147d2d560601601fbf95706ddcc"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">theta</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">Ind</span></a> <a class="idref" href="mathcomp.character.classfun.html#7bc57e92f437fcd76c7df4bf9bcc478d"><span class="id" title="notation">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#640778742e86daa97d31c9911c679af3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#640778742e86daa97d31c9911c679af3"><span class="id" title="notation">sum_b</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ca13a32469ebe56c9f4cc99d00e8eeba"><span class="id" title="notation">]</span></a>.<br/>
+
+<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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_s</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c7768147d2d560601601fbf95706ddcc"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span> <span class="id" title="var">t</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#8a6676f8c04cf9604fb18ba68e59d8fb"><span class="id" title="notation">[\/</span></a> <a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/8.8.0/stdlib//Coq.ssr.ssrbool.html#8a6676f8c04cf9604fb18ba68e59d8fb"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">e</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">p</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&amp;</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#4c362bcf0e947e2792a2e6989b44aeb0"><span class="id" title="notation">^</span></a> 2)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#t"><span class="id" title="variable">t</span></a><br/>
+&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#8a6676f8c04cf9604fb18ba68e59d8fb"><span class="id" title="notation">|</span></a>  <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">p</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">&lt;</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#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#8a6676f8c04cf9604fb18ba68e59d8fb"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_s</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#35b1d00e5e5e2717dc939e30899b07cc"><span class="id" title="notation">[\/</span></a> <a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/>
+&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#35b1d00e5e5e2717dc939e30899b07cc"><span class="id" title="notation">|</span></a>  <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">c</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.inertia.html#c"><span class="id" title="variable">c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ce4524e329c3846bb0bf4371af82a0b8"><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#ce4524e329c3846bb0bf4371af82a0b8"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">&lt;</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#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#35b1d00e5e5e2717dc939e30899b07cc"><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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_s</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">{</span></a><span class="id" title="var">t</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_t</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_s</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">}</span></a>.<br/>
+
+<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/>
+&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">let</span> <span class="id" title="var">theta</span> := <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_u</span></a> <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_c0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">c</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi_c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.character.character.html#cfDet"><span class="id" title="definition">cfDet</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#mu"><span class="id" title="variable">mu</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&amp;</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">c1</span>, <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi_c1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_c1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_s</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c7768147d2d560601601fbf95706ddcc"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#coprime"><span class="id" title="definition">coprime</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.fintype.html#e1fcc6c8b4370f06a39f9b1b3c9764b2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#e1fcc6c8b4370f06a39f9b1b3c9764b2"><span class="id" title="notation">∃</span></a> <span class="id" title="var">c</span><a class="idref" href="mathcomp.ssreflect.fintype.html#46e5a4123d46e6b126f7788a77176785"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">_c</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><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#e1fcc6c8b4370f06a39f9b1b3c9764b2"><span class="id" title="notation">]</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#e1fcc6c8b4370f06a39f9b1b3c9764b2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#e1fcc6c8b4370f06a39f9b1b3c9764b2"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="mathcomp.ssreflect.fintype.html#46e5a4123d46e6b126f7788a77176785"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">_u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><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#e1fcc6c8b4370f06a39f9b1b3c9764b2"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="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/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.prime.html#041d58b37e83f44180445b7edc4ecdfd"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#041d58b37e83f44180445b7edc4ecdfd"><span class="id" title="notation">pi</span></a><a class="idref" href="mathcomp.ssreflect.prime.html#041d58b37e83f44180445b7edc4ecdfd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><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#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span><a class="idref" href="mathcomp.ssreflect.prime.html#041d58b37e83f44180445b7edc4ecdfd"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#fe60c20831f772c0c3c288abf68cc42a"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">Hp</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#fe60c20831f772c0c3c288abf68cc42a"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#ExtendInvariantIrr.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#fe60c20831f772c0c3c288abf68cc42a"><span class="id" title="notation">,</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.inertia.html#N"><span class="id" title="variable">N</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#Hp"><span class="id" title="variable">Hp</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#Hp"><span class="id" title="variable">Hp</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">&amp;</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#43f075314fcfccdaa8a5813debe2d9ed"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#43f075314fcfccdaa8a5813debe2d9ed"><span class="id" title="notation">Sylow</span></a><a class="idref" href="mathcomp.solvable.pgroup.html#43f075314fcfccdaa8a5813debe2d9ed"><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#c7768147d2d560601601fbf95706ddcc"><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#43f075314fcfccdaa8a5813debe2d9ed"><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#c7768147d2d560601601fbf95706ddcc"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">]</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#fe60c20831f772c0c3c288abf68cc42a"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Hp</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">_u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><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#ab1067cd7f1fe17a749116aa49a846b7"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#1e40fee506a85b20590ef299005b003d"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><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#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">u</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">_u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_u</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><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#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">&amp;</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">v</span>,<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi_v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_v</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_t</span></a>) :<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#c27c638e534bbb5b7de2d4b4aa0a3e82"><span class="id" title="notation">&lt;|</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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#c7768147d2d560601601fbf95706ddcc"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">I</span></a><a class="idref" href="mathcomp.character.inertia.html#454089fa36b980e0a936e7f532a99179"><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#454089fa36b980e0a936e7f532a99179"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> (<a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><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#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#697e4695610f677ae98a52af81f779d2"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">c</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">G</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">_c</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.inertia.html#theta"><span class="id" title="variable">theta</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_c</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><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#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">&amp;</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">d</span>,<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">Res</span></a> <a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#e5b5a52e71d080767a6b19226df281de"><span class="id" title="notation">chi_d</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><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#f65ecb5148d1ef5a9c551827b20e9bfa"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">o</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_d</span></a><a class="idref" href="mathcomp.character.character.html#60460a7eea40508f0441a95b4f92e892"><span class="id" title="notation">)</span></a>%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><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#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.inertia.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#ab072eb546972c7e5cdaf33b8a35ce6b"><span class="id" title="notation">}</span></a>).<br/>
+
+<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#d4e6bc74ab587888a04843e00b93ce8e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#d4e6bc74ab587888a04843e00b93ce8e"><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#d4e6bc74ab587888a04843e00b93ce8e"><span class="id" title="notation">with</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#d4e6bc74ab587888a04843e00b93ce8e"><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#d4e6bc74ab587888a04843e00b93ce8e"><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#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">I_G</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><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#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#18b59bdb60cfba8ef35899cef605f5f1"><span class="id" title="notation">_i</span></a><a class="idref" href="mathcomp.character.inertia.html#0e30e69542492ea333fdb332a7a36e8f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.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#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">i</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.inertia.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><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#67c06efe89e9768b37a53c6a4f48ce89"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_i</span></a>)<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><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#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfker"><span class="id" title="definition">cfker</span></a> <a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#04ab09ba1579a4628398b1ac594f25e6"><span class="id" title="notation">chi_j</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><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>
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+\ No newline at end of file
author	Enrico Tassi	2018-04-20 10:54:22 +0200
committer	Enrico Tassi	2018-04-20 10:54:22 +0200
commit	ed05182cece6bb3706e09b2ce14af4a41a2e8141 (patch)
tree	e850d7314b6372d0476cf2ffaf7d3830721db7b1 /docs/htmldoc/mathcomp.character.inertia.html
parent	3d196f44681fb3b23ff8a79fbd44e12308680531 (diff)