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diff --git a/docs/htmldoc/mathcomp.character.vcharacter.html b/docs/htmldoc/mathcomp.character.vcharacter.html new file mode 100644 index 0000000..4b01b7a --- /dev/null +++ b/docs/htmldoc/mathcomp.character.vcharacter.html @@ -0,0 +1,658 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> +<link href="coqdoc.css" rel="stylesheet" type="text/css" /> +<title>mathcomp.character.vcharacter</title> +</head> + +<body> + +<div id="page"> + +<div id="header"> +</div> + +<div id="main"> + +<h1 class="libtitle">Library mathcomp.character.vcharacter</h1> + +<div class="code"> +<span class="comment">(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. <br/> + Distributed under the terms of CeCILL-B. *)</span><br/> +<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="mathcomp.ssreflect.ssreflect.html#"><span class="id" title="library">mathcomp.ssreflect.ssreflect</span></a>.<br/> + +<br/> +<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 provides basic notions of virtual character theory: + 'Z[S, A] == collective predicate for the phi that are Z-linear + combinations of elements of S : seq 'CF(G) and have + support in A : {set gT}. + 'Z[S] == collective predicate for the Z-linear combinations of + elements of S. + 'Z[irr G] == the collective predicate for virtual characters. + dirr G == the collective predicate for normal virtual characters, + i.e., virtual characters of norm 1: + mu \in dirr G <=> m \in 'Z[irr G] and ' [mu] = 1 + <=> mu or - mu \in irr G. +> othonormal subsets of 'Z[irr G] are contained in dirr G. + dIirr G == an index type for normal virtual characters. + dchi i == the normal virtual character of index i. + of_irr i == the (unique) irreducible constituent of dchi i: + dchi i = 'chi(of_irr i) or - 'chi(of_irr i). + ndirr i == the index of - dchi i. + dirr1 G == the normal virtual character index of 1 : 'CF(G), the + principal character. + dirr_dIirr j f == the index i (or dirr1 G if it does not exist) such that + dchi i = f j. + dirr_constt phi == the normal virtual character constituents of phi: + i \in dirr_constt phi <=> [dchi i, phi] > 0. + to_dirr phi i == the normal virtual character constituent of phi with an + irreducible constituent i, when i \in irr_constt phi. +</div> +<div class="code"> + +<br/> +<span class="id" title="keyword">Section</span> <a name="Basics"><span class="id" title="section">Basics</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="Basics.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="Basics.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.vcharacter.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="Basics.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.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>) (<a name="Basics.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="Zchar"><span class="id" title="definition">Zchar</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred_class"><span class="id" title="abbreviation">pred_class</span></a> :=<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#de871826ce6370a1556511e2ea704fe8"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#de871826ce6370a1556511e2ea704fe8"><span class="id" title="notation">pred</span></a> <span class="id" title="var">phi</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#de871826ce6370a1556511e2ea704fe8"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Basics.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Basics.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#de871826ce6370a1556511e2ea704fe8"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.field.algnum.html#dec_Cint_span"><span class="id" title="lemma">dec_Cint_span</span></a> (<a class="idref" href="mathcomp.ssreflect.tuple.html#in_tuple"><span class="id" title="definition">in_tuple</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Basics.S"><span class="id" title="variable">S</span></a>) <a class="idref" href="mathcomp.character.vcharacter.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#de871826ce6370a1556511e2ea704fe8"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Fact</span> <a name="Zchar_key"><span class="id" title="lemma">Zchar_key</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred_key"><span class="id" title="inductive">pred_key</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar"><span class="id" title="definition">Zchar</span></a>. <br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">Zchar_keyed</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#KeyedPred"><span class="id" title="definition">KeyedPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar_key"><span class="id" title="lemma">Zchar_key</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfun0_zchar"><span class="id" title="lemma">cfun0_zchar</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.vcharacter.html#Zchar"><span class="id" title="definition">Zchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Fact</span> <a name="Zchar_zmod"><span class="id" title="lemma">Zchar_zmod</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmod_closed"><span class="id" title="abbreviation">zmod_closed</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar"><span class="id" title="definition">Zchar</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">Zchar_opprPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.OpprPred"><span class="id" title="definition">OpprPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar_zmod"><span class="id" title="lemma">Zchar_zmod</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">Zchar_addrPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.AddrPred"><span class="id" title="definition">AddrPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar_zmod"><span class="id" title="lemma">Zchar_zmod</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">Zchar_zmodPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.ZmodPred"><span class="id" title="definition">ZmodPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar_zmod"><span class="id" title="lemma">Zchar_zmod</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="scale_zchar"><span class="id" title="lemma">scale_zchar</span></a> <span class="id" title="var">a</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.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.vcharacter.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.vcharacter.html#Zchar"><span class="id" title="definition">Zchar</span></a> <a class="idref" href="http://coq.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.vcharacter.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.vcharacter.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.vcharacter.html#Zchar"><span class="id" title="definition">Zchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#Basics"><span class="id" title="section">Basics</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">"</span></a>''Z[' S , A ]" := (<a class="idref" href="mathcomp.character.vcharacter.html#Zchar"><span class="id" title="definition">Zchar</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span>)<br/> + (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''Z[' S , A ]") : <span class="id" title="var">group_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">"</span></a>''Z[' S ]" := <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><span class="id" title="var">S</span><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><br/> + (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8, <span class="id" title="var">format</span> "''Z[' S ]") : <span class="id" title="var">group_scope</span>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="Zchar"><span class="id" title="section">Zchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="Zchar.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="Zchar.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.vcharacter.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">Types</span> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar.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">S</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.html#Zchar.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="zchar_split"><span class="id" title="lemma">zchar_split</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zcharD1E"><span class="id" title="lemma">zcharD1E</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zcharD1"><span class="id" title="lemma">zcharD1</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">S</span> <span class="id" title="var">A</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zcharW"><span class="id" title="lemma">zcharW</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_on"><span class="id" title="lemma">zchar_on</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_onS"><span class="id" title="lemma">zchar_onS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#826eae8d7598a787ea56f4249e6e210e"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_onG"><span class="id" title="lemma">zchar_onG</span></a> <span class="id" title="var">S</span> : <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="irr_vchar_on"><span class="id" title="lemma">irr_vchar_on</span></a> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="support_zchar"><span class="id" title="lemma">support_zchar</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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.algebra.ssralg.html#support"><span class="id" title="abbreviation">support</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</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.vcharacter.html#A"><span class="id" title="variable">A</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="mem_zchar_on"><span class="id" title="lemma">mem_zchar_on</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> <span class="id" title="var">phi</span> : <br/> + <a class="idref" href="mathcomp.character.vcharacter.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.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.classfun.html#98d2bf34d82aa4f9a1163621bbcbea56"><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.vcharacter.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.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +</div> + +<div class="doc"> + A special lemma is needed because trivial fails to use the cfun_onT Hint. +</div> +<div class="code"> +<span class="id" title="keyword">Lemma</span> <a name="mem_zchar"><span class="id" title="lemma">mem_zchar</span></a> <span class="id" title="var">S</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_nth_expansion"><span class="id" title="lemma">zchar_nth_expansion</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">|</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.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"><</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9625b440a0052f6dbfd015f5bb8b5125"><span class="id" title="notation">`</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9625b440a0052f6dbfd015f5bb8b5125"><span class="id" title="notation">_i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_tuple_expansion"><span class="id" title="lemma">zchar_tuple_expansion</span></a> <span class="id" title="var">n</span> (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#d8866adbd4a602b7b4cc275d73486ace"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#d8866adbd4a602b7b4cc275d73486ace"><span class="id" title="notation">tuple</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.vcharacter.html#Zchar.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>) <span class="id" title="var">A</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">|</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.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"><</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b2bfc5b99c28e2c89b336d5f86347706"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9625b440a0052f6dbfd015f5bb8b5125"><span class="id" title="notation">`</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9625b440a0052f6dbfd015f5bb8b5125"><span class="id" title="notation">_i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +</div> + +<div class="doc"> + A pure seq version with the extra hypothesis of S's unicity. +</div> +<div class="code"> +<span class="id" title="keyword">Lemma</span> <a name="zchar_expansion"><span class="id" title="lemma">zchar_expansion</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">|</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">xi</span>, <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></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.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_span"><span class="id" title="lemma">zchar_span</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.vector.html#dd838ef568fa7ae0628a7427a23d7215"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.vector.html#dd838ef568fa7ae0628a7427a23d7215"><span class="id" title="notation">>></span></a>%<span class="id" title="var">VS</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_trans"><span class="id" title="lemma">zchar_trans</span></a> <span class="id" title="var">S1</span> <span class="id" title="var">S2</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="http://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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_trans_on"><span class="id" title="lemma">zchar_trans_on</span></a> <span class="id" title="var">S1</span> <span class="id" title="var">S2</span> <span class="id" title="var">A</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="http://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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_sub_irr"><span class="id" title="lemma">zchar_sub_irr</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="http://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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_subset"><span class="id" title="lemma">zchar_subset</span></a> <span class="id" title="var">S1</span> <span class="id" title="var">S2</span> <span class="id" title="var">A</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="http://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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_subseq"><span class="id" title="lemma">zchar_subseq</span></a> <span class="id" title="var">S1</span> <span class="id" title="var">S2</span> <span class="id" title="var">A</span> :<br/> + <a class="idref" href="mathcomp.ssreflect.seq.html#subseq"><span class="id" title="definition">subseq</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S1"><span class="id" title="variable">S1</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S2"><span class="id" title="variable">S2</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_filter"><span class="id" title="lemma">zchar_filter</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</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.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.vcharacter.html#Zchar.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/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#filter"><span class="id" title="definition">filter</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar"><span class="id" title="section">Zchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="VChar"><span class="id" title="section">VChar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="VChar.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="VChar.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.vcharacter.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">Types</span> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.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> <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.vcharacter.html#VChar.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>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.html#VChar.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="char_vchar"><span class="id" title="lemma">char_vchar</span></a> <span class="id" title="var">chi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="irr_vchar"><span class="id" title="lemma">irr_vchar</span></a> <span class="id" title="var">i</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.vcharacter.html#VChar.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.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfun1_vchar"><span class="id" title="lemma">cfun1_vchar</span></a> : 1 <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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>. <br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="vcharP"><span class="id" title="lemma">vcharP</span></a> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">chi1</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.vcharacter.html#chi1"><span class="id" title="variable">chi1</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><br/> + <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#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">chi2</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.vcharacter.html#chi2"><span class="id" title="variable">chi2</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#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#chi1"><span class="id" title="variable">chi1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d70623330b2787db6b196e37db7d8f45"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#chi2"><span class="id" title="variable">chi2</span></a>)<br/> + (<a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Aint_vchar"><span class="id" title="lemma">Aint_vchar</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algnum.html#Aint"><span class="id" title="definition">Aint</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Cint_vchar1"><span class="id" title="lemma">Cint_vchar1</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> 1%<span class="id" title="var">g</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.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Cint_cfdot_vchar_irr"><span class="id" title="lemma">Cint_cfdot_vchar_irr</span></a> <span class="id" title="var">i</span> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <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="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.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_vchar_r"><span class="id" title="lemma">cfdot_vchar_r</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.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="http://coq.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_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.vcharacter.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> <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.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><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.vcharacter.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.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>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Cint_cfdot_vchar"><span class="id" title="lemma">Cint_cfdot_vchar</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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span>, <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.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="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.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</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="Cnat_cfnorm_vchar"><span class="id" title="lemma">Cnat_cfnorm_vchar</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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span>, <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cnat"><span class="id" title="definition">Cnat</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/> + +<br/> +<span class="id" title="keyword">Fact</span> <a name="vchar_mulr_closed"><span class="id" title="lemma">vchar_mulr_closed</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.mulr_closed"><span class="id" title="abbreviation">mulr_closed</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">vchar_mulrPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.MulrPred"><span class="id" title="definition">MulrPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#vchar_mulr_closed"><span class="id" title="lemma">vchar_mulr_closed</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">vchar_smulrPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.SmulrPred"><span class="id" title="definition">SmulrPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#vchar_mulr_closed"><span class="id" title="lemma">vchar_mulr_closed</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">vchar_semiringPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.SemiringPred"><span class="id" title="definition">SemiringPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#vchar_mulr_closed"><span class="id" title="lemma">vchar_mulr_closed</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">vchar_subringPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.SubringPred"><span class="id" title="definition">SubringPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#vchar_mulr_closed"><span class="id" title="lemma">vchar_mulr_closed</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="mul_vchar"><span class="id" title="lemma">mul_vchar</span></a> <span class="id" title="var">A</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span>, <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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">Section</span> <a name="VChar.CfdotPairwiseOrthogonal"><span class="id" title="section">CfdotPairwiseOrthogonal</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="VChar.CfdotPairwiseOrthogonal.M"><span class="id" title="variable">M</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.vcharacter.html#VChar.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="VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.html#VChar.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 name="VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</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.vcharacter.html#VChar.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.vcharacter.html#M"><span class="id" title="variable">M</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>).<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="VChar.CfdotPairwiseOrthogonal.Inu"><span class="id" title="variable">Inu</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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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="mathcomp.character.classfun.html#isometry"><span class="id" title="definition">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</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 name="VChar.CfdotPairwiseOrthogonal.oSS"><span class="id" title="variable">oSS</span></a> : <a class="idref" href="mathcomp.character.classfun.html#pairwise_orthogonal"><span class="id" title="definition">pairwise_orthogonal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfdotPairwiseOrthogonal.freeS"><span class="id" title="variable">freeS</span></a> := <a class="idref" href="mathcomp.character.classfun.html#orthogonal_free"><span class="id" title="lemma">orthogonal_free</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.oSS"><span class="id" title="variable">oSS</span></a>.<br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfdotPairwiseOrthogonal.uniqS"><span class="id" title="variable">uniqS</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.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a> := <a class="idref" href="mathcomp.algebra.vector.html#free_uniq"><span class="id" title="lemma">free_uniq</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.freeS"><span class="id" title="variable">freeS</span></a>.<br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfdotPairwiseOrthogonal.Z_S"><span class="id" title="variable">Z_S</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>. <br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfdotPairwiseOrthogonal.notS0"><span class="id" title="variable">notS0</span></a> : 0 <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.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a>. <br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfdotPairwiseOrthogonal.dotSS"><span class="id" title="variable">dotSS</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#proj2"><span class="id" title="lemma">proj2</span></a> (<a class="idref" href="mathcomp.character.classfun.html#pairwise_orthogonalP"><span class="id" title="lemma">pairwise_orthogonalP</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.oSS"><span class="id" title="variable">oSS</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="map_pairwise_orthogonal"><span class="id" title="lemma">map_pairwise_orthogonal</span></a> : <a class="idref" href="mathcomp.character.classfun.html#pairwise_orthogonal"><span class="id" title="definition">pairwise_orthogonal</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfproj_sum_orthogonal"><span class="id" title="lemma">cfproj_sum_orthogonal</span></a> <span class="id" title="var">P</span> <span class="id" title="var">z</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#cbc2f2ab11c1c376b5c4511d28b14d74"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#cbc2f2ab11c1c376b5c4511d28b14d74"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#cbc2f2ab11c1c376b5c4511d28b14d74"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.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/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><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">else</span></a> 0.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_sum_orthogonal"><span class="id" title="lemma">cfdot_sum_orthogonal</span></a> <span class="id" title="var">z1</span> <span class="id" title="var">z2</span> :<br/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z1"><span class="id" title="variable">z1</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</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#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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z2"><span class="id" title="variable">z2</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z1"><span class="id" title="variable">z1</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#z2"><span class="id" title="variable">z2</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><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.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfnorm_sum_orthogonal"><span class="id" title="lemma">cfnorm_sum_orthogonal</span></a> <span class="id" title="var">z</span> :<br/> + <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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#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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#c536f9a86d3c053391521360ac3f5a61"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#c536f9a86d3c053391521360ac3f5a61"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">^+</span></a> 2 <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfnorm_orthogonal"><span class="id" title="lemma">cfnorm_orthogonal</span></a> : <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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#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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal"><span class="id" title="section">CfdotPairwiseOrthogonal</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="orthogonal_span"><span class="id" title="lemma">orthogonal_span</span></a> <span class="id" title="var">S</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.classfun.html#pairwise_orthogonal"><span class="id" title="definition">pairwise_orthogonal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.algebra.vector.html#dd838ef568fa7ae0628a7427a23d7215"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.vector.html#dd838ef568fa7ae0628a7427a23d7215"><span class="id" title="notation">>></span></a>%<span class="id" title="var">VS</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/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="keyword">fun</span> <span class="id" title="var">xi</span> ⇒ <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</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#4fa85b0aa898c2a7e18c3b076438c2e7"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="VChar.CfDotOrthonormal"><span class="id" title="section">CfDotOrthonormal</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="VChar.CfDotOrthonormal.M"><span class="id" title="variable">M</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.vcharacter.html#VChar.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="VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.html#VChar.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 name="VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</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.vcharacter.html#VChar.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.vcharacter.html#M"><span class="id" title="variable">M</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><span class="id" title="notation">)</span></a>).<br/> +<span class="id" title="keyword">Hypotheses</span> (<a name="VChar.CfDotOrthonormal.Inu"><span class="id" title="variable">Inu</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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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="mathcomp.character.classfun.html#isometry"><span class="id" title="definition">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</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 name="VChar.CfDotOrthonormal.onS"><span class="id" title="variable">onS</span></a> : <a class="idref" href="mathcomp.character.classfun.html#orthonormal"><span class="id" title="definition">orthonormal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a>).<br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfDotOrthonormal.oSS"><span class="id" title="variable">oSS</span></a> := <a class="idref" href="mathcomp.character.classfun.html#orthonormal_orthogonal"><span class="id" title="lemma">orthonormal_orthogonal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.onS"><span class="id" title="variable">onS</span></a>.<br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfDotOrthonormal.freeS"><span class="id" title="variable">freeS</span></a> := <a class="idref" href="mathcomp.character.classfun.html#orthogonal_free"><span class="id" title="lemma">orthogonal_free</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.oSS"><span class="id" title="variable">oSS</span></a>.<br/> +<span class="id" title="keyword">Let</span> <a name="VChar.CfDotOrthonormal.nS1"><span class="id" title="variable">nS1</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.vcharacter.html#VChar.CfDotOrthonormal.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> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span>, <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="map_orthonormal"><span class="id" title="lemma">map_orthonormal</span></a> : <a class="idref" href="mathcomp.character.classfun.html#orthonormal"><span class="id" title="definition">orthonormal</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfproj_sum_orthonormal"><span class="id" title="lemma">cfproj_sum_orthonormal</span></a> <span class="id" title="var">z</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="http://coq.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.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_sum_orthonormal"><span class="id" title="lemma">cfdot_sum_orthonormal</span></a> <span class="id" title="var">z1</span> <span class="id" title="var">z2</span> :<br/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z1"><span class="id" title="variable">z1</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</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#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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z2"><span class="id" title="variable">z2</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z1"><span class="id" title="variable">z1</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#z2"><span class="id" title="variable">z2</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><span class="id" title="notation">)^*</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfnorm_sum_orthonormal"><span class="id" title="lemma">cfnorm_sum_orthonormal</span></a> <span class="id" title="var">z</span> :<br/> + <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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#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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#c536f9a86d3c053391521360ac3f5a61"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#c536f9a86d3c053391521360ac3f5a61"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">^+</span></a> 2.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfnorm_map_orthonormal"><span class="id" title="lemma">cfnorm_map_orthonormal</span></a> : <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</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">Lemma</span> <a name="orthonormal_span"><span class="id" title="lemma">orthonormal_span</span></a> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.algebra.vector.html#dd838ef568fa7ae0628a7427a23d7215"><span class="id" title="notation"><<</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.vector.html#dd838ef568fa7ae0628a7427a23d7215"><span class="id" title="notation">>></span></a>%<span class="id" title="var">VS</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/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="keyword">fun</span> <span class="id" title="var">xi</span> ⇒ <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</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.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#f5350ad671d3ce0e1e463e298917cf6e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal"><span class="id" title="section">CfDotOrthonormal</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfnorm_orthonormal"><span class="id" title="lemma">cfnorm_orthonormal</span></a> <span class="id" title="var">S</span> :<br/> + <a class="idref" href="mathcomp.character.classfun.html#orthonormal"><span class="id" title="definition">orthonormal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</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">Lemma</span> <a name="vchar_orthonormalP"><span class="id" title="lemma">vchar_orthonormalP</span></a> <span class="id" title="var">S</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="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">I</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.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.seq.html#perm_eq"><span class="id" title="definition">perm_eq</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</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.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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_i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">|</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb029fd23b6fc39e014fe7658d797041"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.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>)<br/> + (<a class="idref" href="mathcomp.character.classfun.html#orthonormal"><span class="id" title="definition">orthonormal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="vchar_norm1P"><span class="id" title="lemma">vchar_norm1P</span></a> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">b</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</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> <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">i</span> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#b"><span class="id" title="variable">b</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_i</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="zchar_small_norm"><span class="id" title="lemma">zchar_small_norm</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">n</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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.vcharacter.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="http://coq.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.vcharacter.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#989c98e7ddd65d5bf37c334ff2076de8"><span class="id" title="notation"><</span></a> 4)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">{</span></a><span class="id" title="var">S</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#d8866adbd4a602b7b4cc275d73486ace"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#d8866adbd4a602b7b4cc275d73486ace"><span class="id" title="notation">tuple</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.vcharacter.html#VChar.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.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">|</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.classfun.html#orthonormal"><span class="id" title="definition">orthonormal</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="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.vcharacter.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.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">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#c9afba1af653123a1dddfe925d2b3ab3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#xi"><span class="id" title="variable">xi</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="vchar_norm2"><span class="id" title="lemma">vchar_norm2</span></a> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 2<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="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">i</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">j</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.vcharacter.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#28b18e493f7cb0bd8447607bdc385ff8"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.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.algebra.ssralg.html#d70623330b2787db6b196e37db7d8f45"><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>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#VChar"><span class="id" title="section">VChar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="Isometries"><span class="id" title="section">Isometries</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="Isometries.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="Isometries.L"><span class="id" title="variable">L</span></a> <a name="Isometries.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.vcharacter.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="Isometries.S"><span class="id" title="variable">S</span></a> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#d35bff44a2e44c0688f93d605f17e822"><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">nu</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#6566b94c06c342b0768c3d2d73badf6e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6566b94c06c342b0768c3d2d73badf6e"><span class="id" title="notation">additive</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.vcharacter.html#Isometries.L"><span class="id" title="variable">L</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.vcharacter.html#Isometries.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="mathcomp.algebra.ssralg.html#6566b94c06c342b0768c3d2d73badf6e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Zisometry_of_cfnorm"><span class="id" title="lemma">Zisometry_of_cfnorm</span></a> (<span class="id" title="var">tauS</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.html#Isometries.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/> + <a class="idref" href="mathcomp.character.classfun.html#pairwise_orthogonal"><span class="id" title="definition">pairwise_orthogonal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#pairwise_orthogonal"><span class="id" title="definition">pairwise_orthogonal</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tauS"><span class="id" title="variable">tauS</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfnorm"><span class="id" title="abbreviation">cfnorm</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tauS"><span class="id" title="variable">tauS</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.character.classfun.html#cfnorm"><span class="id" title="abbreviation">cfnorm</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tauS"><span class="id" title="variable">tauS</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">{</span></a><span class="id" title="var">tau</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#697e59dccfd7ad4519680ddb16ef82da"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#697e59dccfd7ad4519680ddb16ef82da"><span class="id" title="notation">linear</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.vcharacter.html#Isometries.L"><span class="id" title="variable">L</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.vcharacter.html#Isometries.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="mathcomp.algebra.ssralg.html#697e59dccfd7ad4519680ddb16ef82da"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tau"><span class="id" title="variable">tau</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tauS"><span class="id" title="variable">tauS</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tau"><span class="id" title="variable">tau</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">to</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Zisometry_of_iso"><span class="id" title="lemma">Zisometry_of_iso</span></a> <span class="id" title="var">f</span> :<br/> + <a class="idref" href="mathcomp.algebra.vector.html#free"><span class="id" title="definition">free</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">to</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">{</span></a><span class="id" title="var">tau</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#697e59dccfd7ad4519680ddb16ef82da"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#697e59dccfd7ad4519680ddb16ef82da"><span class="id" title="notation">linear</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.vcharacter.html#Isometries.L"><span class="id" title="variable">L</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.vcharacter.html#Isometries.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="mathcomp.algebra.ssralg.html#697e59dccfd7ad4519680ddb16ef82da"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><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.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tau"><span class="id" title="variable">tau</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.vcharacter.html#f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#tau"><span class="id" title="variable">tau</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">to</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#a599128736d70e142550ed6520a98950"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#602b9943a639fb973abed6e2c7854421"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Zisometry_inj"><span class="id" title="lemma">Zisometry_inj</span></a> <span class="id" title="var">A</span> <span class="id" title="var">nu</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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="mathcomp.character.classfun.html#isometry"><span class="id" title="definition">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#nu"><span class="id" title="variable">nu</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="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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#nu"><span class="id" title="variable">nu</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="isometry_in_zchar"><span class="id" title="lemma">isometry_in_zchar</span></a> <span class="id" title="var">nu</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.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <a class="idref" href="mathcomp.character.classfun.html#isometry"><span class="id" title="definition">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#nu"><span class="id" title="variable">nu</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="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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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="mathcomp.character.classfun.html#isometry"><span class="id" title="definition">isometry</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#nu"><span class="id" title="variable">nu</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">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries"><span class="id" title="section">Isometries</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="AutVchar"><span class="id" title="section">AutVchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="AutVchar.u"><span class="id" title="variable">u</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#0c709ebe43ddbd7719f75250a7b916d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c709ebe43ddbd7719f75250a7b916d9"><span class="id" title="notation">rmorphism</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.algC"><span class="id" title="abbreviation">algC</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.algC"><span class="id" title="abbreviation">algC</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c709ebe43ddbd7719f75250a7b916d9"><span class="id" title="notation">}</span></a>) (<a name="AutVchar.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="AutVchar.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.vcharacter.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">S</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</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.vcharacter.html#AutVchar.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>) (<span class="id" title="var">phi</span> <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.vcharacter.html#AutVchar.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="cfAut_zchar"><span class="id" title="lemma">cfAut_zchar</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> <span class="id" title="var">psi</span> : <br/> + <a class="idref" href="mathcomp.character.classfun.html#cfAut_closed"><span class="id" title="definition">cfAut_closed</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#AutVchar.u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfAut_vchar"><span class="id" title="lemma">cfAut_vchar</span></a> <span class="id" title="var">A</span> <span class="id" title="var">psi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sub_aut_zchar"><span class="id" title="lemma">sub_aut_zchar</span></a> <span class="id" title="var">S</span> <span class="id" title="var">A</span> <span class="id" title="var">psi</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.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.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d70623330b2787db6b196e37db7d8f45"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="conjC_vcharAut"><span class="id" title="lemma">conjC_vcharAut</span></a> <span class="id" title="var">chi</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#AutVchar.u"><span class="id" title="variable">u</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="mathcomp.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><span class="id" title="notation">)^*</span></a> <a class="idref" href="http://coq.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.vcharacter.html#AutVchar.u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#b07d6e6599ef6e468ce182ffe6029532"><span class="id" title="notation">)^*</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_aut_vchar"><span class="id" title="lemma">cfdot_aut_vchar</span></a> <span class="id" title="var">phi</span> <span class="id" title="var">chi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">u</span></a> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#chi"><span class="id" title="variable">chi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">u</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.vcharacter.html#AutVchar.u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#chi"><span class="id" title="variable">chi</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="vchar_aut"><span class="id" title="lemma">vchar_aut</span></a> <span class="id" title="var">A</span> <span class="id" title="var">chi</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.vcharacter.html#chi"><span class="id" title="variable">chi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#be5305d56f36ee4c1e372520d7a4ee16"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a class="idref" href="http://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.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a><a 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">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#AutVchar"><span class="id" title="section">AutVchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="cfConjC_vchar"><span class="id" title="definition">cfConjC_vchar</span></a> := <a class="idref" href="mathcomp.character.vcharacter.html#cfAut_vchar"><span class="id" title="lemma">cfAut_vchar</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.Theory.conjC"><span class="id" title="definition">conjC</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="MoreVchar"><span class="id" title="section">MoreVchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="MoreVchar.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="MoreVchar.G"><span class="id" title="variable">G</span></a> <a name="MoreVchar.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.vcharacter.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="cfRes_vchar"><span class="id" title="lemma">cfRes_vchar</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#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.vcharacter.html#MoreVchar.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.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfRes_vchar_on"><span class="id" title="lemma">cfRes_vchar_on</span></a> <span class="id" title="var">A</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.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.vcharacter.html#MoreVchar.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.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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#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.vcharacter.html#MoreVchar.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.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfInd_vchar"><span class="id" title="lemma">cfInd_vchar</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#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.vcharacter.html#MoreVchar.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.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="sub_conjC_vchar"><span class="id" title="lemma">sub_conjC_vchar</span></a> <span class="id" title="var">A</span> <span class="id" title="var">phi</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><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.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d70623330b2787db6b196e37db7d8f45"><span class="id" title="notation">-</span></a> (<a class="idref" href="mathcomp.character.vcharacter.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>)%<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.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">[</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.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#adb8044960c962a921cca1bd48aae97d"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#7c3f95d2f977365e6189f41b3274d94e"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Frobenius_kernel_exists"><span class="id" title="lemma">Frobenius_kernel_exists</span></a> :<br/> + <a class="idref" href="mathcomp.solvable.frobenius.html#9829227212a3e6faf0fd92ec80565912"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#9829227212a3e6faf0fd92ec80565912"><span class="id" title="notation">Frobenius</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#9829227212a3e6faf0fd92ec80565912"><span class="id" title="notation">with</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#9829227212a3e6faf0fd92ec80565912"><span class="id" title="notation">complement</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#9829227212a3e6faf0fd92ec80565912"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">{</span></a><span class="id" title="var">K</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><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.vcharacter.html#MoreVchar.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.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#4d6d07a024def374c6574865fc5ac3d7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#4d6d07a024def374c6574865fc5ac3d7"><span class="id" title="notation">Frobenius</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#4d6d07a024def374c6574865fc5ac3d7"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#4d6d07a024def374c6574865fc5ac3d7"><span class="id" title="notation">><|</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#4d6d07a024def374c6574865fc5ac3d7"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar"><span class="id" title="section">MoreVchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dirr"><span class="id" title="definition">dirr</span></a> (<span class="id" title="var">gT</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.finGroupType"><span class="id" title="abbreviation">finGroupType</span></a>) (<span class="id" title="var">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.vcharacter.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 class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred_class"><span class="id" title="abbreviation">pred_class</span></a> := <br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ba4e2de877832f7c061554da0cb06dd3"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ba4e2de877832f7c061554da0cb06dd3"><span class="id" title="notation">pred</span></a> <span class="id" title="var">f</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ba4e2de877832f7c061554da0cb06dd3"><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.vcharacter.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> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ba4e2de877832f7c061554da0cb06dd3"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#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.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><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.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#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.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ba4e2de877832f7c061554da0cb06dd3"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Section</span> <a name="Norm1vchar"><span class="id" title="section">Norm1vchar</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Variables</span> (<a name="Norm1vchar.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="Norm1vchar.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.vcharacter.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">Fact</span> <a name="dirr_key"><span class="id" title="lemma">dirr_key</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred_key"><span class="id" title="inductive">pred_key</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>). <br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">dirr_keyed</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#KeyedPred"><span class="id" title="definition">KeyedPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_key"><span class="id" title="lemma">dirr_key</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Fact</span> <a name="dirr_oppr_closed"><span class="id" title="lemma">dirr_oppr_closed</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.oppr_closed"><span class="id" title="abbreviation">oppr_closed</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>).<br/> + <span class="id" title="keyword">Canonical</span> <span class="id" title="var">dirr_opprPred</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.OpprPred"><span class="id" title="definition">OpprPred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_oppr_closed"><span class="id" title="lemma">dirr_oppr_closed</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_opp"><span class="id" title="lemma">dirr_opp</span></a> <span class="id" title="var">v</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><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.vcharacter.html#v"><span class="id" title="variable">v</span></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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.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.vcharacter.html#v"><span class="id" title="variable">v</span></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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_sign"><span class="id" title="lemma">dirr_sign</span></a> <span class="id" title="var">n</span> <span class="id" title="var">v</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.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">)^+</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#81f8078534dcbb7e13a32d292f766525"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#v"><span class="id" title="variable">v</span></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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.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.vcharacter.html#v"><span class="id" title="variable">v</span></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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="irr_dirr"><span class="id" title="lemma">irr_dirr</span></a> <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_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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirrP"><span class="id" title="lemma">dirrP</span></a> <span class="id" title="var">f</span> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">b</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</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> <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">i</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.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.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#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#b"><span class="id" title="variable">b</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_i</span></a>) (<a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>).<br/> + +<br/> +</div> + +<div class="doc"> + This should perhaps be the definition of dirr. +</div> +<div class="code"> +<span class="id" title="keyword">Lemma</span> <a name="dirrE"><span class="id" title="lemma">dirrE</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</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.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_dirr"><span class="id" title="lemma">cfdot_dirr</span></a> <span class="id" title="var">f</span> <span class="id" title="var">g</span> : <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.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.vcharacter.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.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/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#g"><span class="id" title="variable">g</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="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><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.vcharacter.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> -1 <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.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#g"><span class="id" title="variable">g</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="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="dirr_norm1"><span class="id" title="lemma">dirr_norm1</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_aut"><span class="id" title="lemma">dirr_aut</span></a> <span class="id" title="var">u</span> <span class="id" title="var">phi</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#cfAut"><span class="id" title="definition">cfAut</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.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.vcharacter.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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dIirr"><span class="id" title="definition">dIirr</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.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) := (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</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.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a>)%<span class="id" title="keyword">type</span>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dirr1"><span class="id" title="definition">dirr1</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.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="ndirr"><span class="id" title="definition">ndirr</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.vcharacter.html#Norm1vchar.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.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a>) : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a> := <br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><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.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c4877bbfe60d8f22b47ac99ace86216a"><span class="id" title="notation">.1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="ndirr_diff"><span class="id" title="lemma">ndirr_diff</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>) : <a class="idref" href="mathcomp.character.vcharacter.html#ndirr"><span class="id" title="definition">ndirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="ndirrK"><span class="id" title="lemma">ndirrK</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> (@<a class="idref" href="mathcomp.character.vcharacter.html#ndirr"><span class="id" title="definition">ndirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="ndirr_inj"><span class="id" title="lemma">ndirr_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> (@<a class="idref" href="mathcomp.character.vcharacter.html#ndirr"><span class="id" title="definition">ndirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dchi"><span class="id" title="definition">dchi</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.vcharacter.html#Norm1vchar.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.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.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><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.vcharacter.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/> + <a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">)^+</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c4877bbfe60d8f22b47ac99ace86216a"><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.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.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dchi1"><span class="id" title="lemma">dchi1</span></a> : <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#dirr1"><span class="id" title="definition">dirr1</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_dchi"><span class="id" title="lemma">dirr_dchi</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dIrrP"><span class="id" title="lemma">dIrrP</span></a> <span class="id" title="var">phi</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="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">i</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.vcharacter.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.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dchi_ndirrE"><span class="id" title="lemma">dchi_ndirrE</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>) : <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#ndirr"><span class="id" title="definition">ndirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_dchi"><span class="id" title="lemma">cfdot_dchi</span></a> (<span class="id" title="var">i</span> <span class="id" title="var">j</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>) : <br/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</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.algebra.ssralg.html#af5c1d7e13410a0a6c3dff5441ac8477"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</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#d70623330b2787db6b196e37db7d8f45"><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.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#ndirr"><span class="id" title="definition">ndirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</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">Lemma</span> <a name="dchi_vchar"><span class="id" title="lemma">dchi_vchar</span></a> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfnorm_dchi"><span class="id" title="lemma">cfnorm_dchi</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>) : <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_inj"><span class="id" title="lemma">dirr_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> (@<a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dirr_dIirr"><span class="id" title="definition">dirr_dIirr</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.vcharacter.html#Norm1vchar.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">J</span> (<span class="id" title="var">f</span> : <a class="idref" href="mathcomp.character.vcharacter.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.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.vcharacter.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>) <span class="id" title="var">j</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a> :=<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#odflt"><span class="id" title="abbreviation">odflt</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#dirr1"><span class="id" title="definition">dirr1</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a>) <a class="idref" href="mathcomp.ssreflect.fintype.html#705e11e709bb3e1492e885a674508f9a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#705e11e709bb3e1492e885a674508f9a"><span class="id" title="notation">pick</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#705e11e709bb3e1492e885a674508f9a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#705e11e709bb3e1492e885a674508f9a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_dIirrPE"><span class="id" title="lemma">dirr_dIirrPE</span></a> <span class="id" title="var">J</span> (<span class="id" title="var">f</span> : <a class="idref" href="mathcomp.character.vcharacter.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.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.vcharacter.html#Norm1vchar.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>) (<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.vcharacter.html#J"><span class="id" title="variable">J</span></a>) :<br/> + <a 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">j</span>, <a class="idref" href="mathcomp.character.vcharacter.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.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.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <span class="id" title="keyword">∀</span> <span class="id" title="var">j</span>, <a class="idref" href="mathcomp.character.vcharacter.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.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.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#dirr_dIirr"><span class="id" title="definition">dirr_dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">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.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_dIirrE"><span class="id" title="lemma">dirr_dIirrE</span></a> <span class="id" title="var">J</span> (<span class="id" title="var">f</span> : <a class="idref" href="mathcomp.character.vcharacter.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.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.vcharacter.html#Norm1vchar.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/> + <a 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">j</span>, <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">j</span>, <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#dirr_dIirr"><span class="id" title="definition">dirr_dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">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.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="dirr_constt"><span class="id" title="definition">dirr_constt</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.vcharacter.html#Norm1vchar.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.vcharacter.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>) : <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.ssreflect.finset.html#0fec877de6d09ef39abb9b599a84eb0e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#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> := <br/> + <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">set</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">|</span></a> 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><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.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#20dd00d77a881552893c96be95088d1a"><span class="id" title="notation">]</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_consttE"><span class="id" title="lemma">dirr_consttE</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.vcharacter.html#Norm1vchar.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>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>) : <br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.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="http://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>0 <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><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.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="Cnat_dirr"><span class="id" title="lemma">Cnat_dirr</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.vcharacter.html#Norm1vchar.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>) <span class="id" title="var">i</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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#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.field.algC.html#Algebraics.Exports.Cnat"><span class="id" title="definition">Cnat</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_constt_oppr"><span class="id" title="lemma">dirr_constt_oppr</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</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.vcharacter.html#Norm1vchar.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/> + <a class="idref" href="http://coq.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.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.character.vcharacter.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="http://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.vcharacter.html#ndirr"><span class="id" title="definition">ndirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.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>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_constt_oppI"><span class="id" title="lemma">dirr_constt_oppI</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.vcharacter.html#Norm1vchar.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/> + <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.character.vcharacter.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.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_constt_oppl"><span class="id" title="lemma">dirr_constt_oppl</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.vcharacter.html#Norm1vchar.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>) <span class="id" title="var">i</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.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> <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="mathcomp.character.vcharacter.html#ndirr"><span class="id" title="definition">ndirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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">\</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.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="to_dirr"><span class="id" title="definition">to_dirr</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.vcharacter.html#Norm1vchar.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.vcharacter.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>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.character.html#Iirr"><span class="id" title="abbreviation">Iirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a>) : <a class="idref" href="mathcomp.character.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a> := <br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <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.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation"><</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="of_irr"><span class="id" title="definition">of_irr</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.vcharacter.html#Norm1vchar.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.vcharacter.html#dIirr"><span class="id" title="definition">dIirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</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.vcharacter.html#B"><span class="id" title="variable">B</span></a> := <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="irr_constt_to_dirr"><span class="id" title="lemma">irr_constt_to_dirr</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.vcharacter.html#Norm1vchar.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>) <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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_constt"><span class="id" title="definition">irr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.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="http://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.vcharacter.html#to_dirr"><span class="id" title="definition">to_dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">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.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.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>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="to_dirrK"><span class="id" title="lemma">to_dirrK</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.vcharacter.html#Norm1vchar.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.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#to_dirr"><span class="id" title="definition">to_dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a>) (@<a class="idref" href="mathcomp.character.vcharacter.html#of_irr"><span class="id" title="definition">of_irr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>).<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="of_irrK"><span class="id" title="lemma">of_irrK</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.vcharacter.html#Norm1vchar.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/> + <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.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (@<a class="idref" href="mathcomp.character.vcharacter.html#of_irr"><span class="id" title="definition">of_irr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a>) (<a class="idref" href="mathcomp.character.vcharacter.html#to_dirr"><span class="id" title="definition">to_dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.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#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_todirrE"><span class="id" title="lemma">cfdot_todirrE</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.vcharacter.html#Norm1vchar.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>) <span class="id" title="var">i</span> (<span class="id" title="var">phi_i</span> := <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#to_dirr"><span class="id" title="definition">to_dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a>)) :<br/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#phi_i"><span class="id" title="variable">phi_i</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.vcharacter.html#phi_i"><span class="id" title="variable">phi_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.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <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.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_i</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfun_sum_dconstt"><span class="id" title="lemma">cfun_sum_dconstt</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.vcharacter.html#Norm1vchar.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/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.character.vcharacter.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.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">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</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.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a>.<br/> +</div> + +<div class="doc"> + GG -- rewrite pattern fails in trunk + move=> PiZ; rewrite [X in X = _ ]cfun_sum_constt. +</div> +<div class="code"> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cnorm_dconstt"><span class="id" title="lemma">cnorm_dconstt</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.vcharacter.html#Norm1vchar.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/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</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.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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#fb22424322c3d7eb9b837dfca65ce21e"><span class="id" title="notation">^+</span></a> 2.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="dirr_small_norm"><span class="id" title="lemma">dirr_small_norm</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.vcharacter.html#Norm1vchar.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>) <span class="id" title="var">n</span> :<br/> + <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><span class="id" title="notation">[</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.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.vcharacter.html#59e10658c474881b37bc0e4c58704272"><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#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#78bbcb69a863dad655ecd2a75fa4ea13"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.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.vcharacter.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="http://coq.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.vcharacter.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#989c98e7ddd65d5bf37c334ff2076de8"><span class="id" title="notation"><</span></a> 4)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</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.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">&</span></a> <br/> + <a class="idref" href="mathcomp.character.vcharacter.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.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">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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">Lemma</span> <a name="cfdot_sum_dchi"><span class="id" title="lemma">cfdot_sum_dchi</span></a> (<span class="id" title="var">phi1</span> <span class="id" title="var">phi2</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.vcharacter.html#Norm1vchar.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/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><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">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi1"><span class="id" title="variable">phi1</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a><br/> + <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">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi2"><span class="id" title="variable">phi2</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0c791dbdc1655ae690f0a6c159a384c0"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dchi"><span class="id" title="definition">dchi</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</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> <br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi1"><span class="id" title="variable">phi1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi2"><span class="id" title="variable">phi2</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#d70623330b2787db6b196e37db7d8f45"><span class="id" title="notation">-</span></a><br/> + <a class="idref" href="mathcomp.ssreflect.fintype.html#f01714bb99e6c7abc6cfb2e43eff7f6e"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi1"><span class="id" title="variable">phi1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cb41714a5a23482f7a48a98975fa8c59"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi2"><span class="id" title="variable">phi2</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>.<br/> + +<br/> +<span class="id" title="keyword">Lemma</span> <a name="cfdot_dirr_eq1"><span class="id" title="lemma">cfdot_dirr_eq1</span></a> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.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> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span> <span class="id" title="var">psi</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#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.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.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.vcharacter.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> <a class="idref" href="mathcomp.character.vcharacter.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="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="cfdot_add_dirr_eq1"><span class="id" title="lemma">cfdot_add_dirr_eq1</span></a> :<br/> + <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#0ebfa8e4076fc95e12536d4b6a76aa07"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#0ebfa8e4076fc95e12536d4b6a76aa07"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr"><span class="id" title="definition">dirr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.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#0ebfa8e4076fc95e12536d4b6a76aa07"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#0ebfa8e4076fc95e12536d4b6a76aa07"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi1</span> <span class="id" title="var">phi2</span> <span class="id" title="var">psi</span>,<br/> + <a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi1"><span class="id" title="variable">phi1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#ae4d81913e6239182a9ac7467ffde8cd"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi2"><span class="id" title="variable">phi2</span></a><a class="idref" href="mathcomp.character.classfun.html#101f65e74897bbc2c1bee8f833b19e33"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.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="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#phi1"><span class="id" title="variable">phi1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#7a45dffb109c3069e5c675be68643e60"><span class="id" title="notation">∨</span></a> <a class="idref" href="mathcomp.character.vcharacter.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.vcharacter.html#phi2"><span class="id" title="variable">phi2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#0ebfa8e4076fc95e12536d4b6a76aa07"><span class="id" title="notation">}</span></a>.<br/> + +<br/> +<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar"><span class="id" title="section">Norm1vchar</span></a>.<br/> +</div> +</div> + +<div id="footer"> +<hr/><a href="index.html">Index</a><hr/>This page has been generated by <a href="http://coq.inria.fr/">coqdoc</a> +</div> + +</div> + +</body> +</html>
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