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<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/>
<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">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/>
<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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<a name="Basics.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="Zchar"><span class="id" title="definition">Zchar</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Basics.B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a> :=<br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">pred</span></a> <span class="id" title="var">phi</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><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/V8.9.0/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/V8.9.0/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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar"><span class="id" title="definition">Zchar</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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="daf4f1487eeda5c7b4c53a78a01e8b57"><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="ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">"</span></a>''Z[' S ]" := <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">[</span></a><span class="id" title="var">S</span><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/>
<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Zchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.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#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><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#62c6c4bf7772487a11a35ed29aee9fc7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.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#784f0af919f467115774be372bf0dbd7"><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#3b05480e39db306e67fadbc79d394529"><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#82d810f9f90b79e8fe98d90a63070c32"><span class="id" title="notation">`</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#82d810f9f90b79e8fe98d90a63070c32"><span class="id" title="notation">_i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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#c3913abe839346eb60d82da74b0b1f67"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#c3913abe839346eb60d82da74b0b1f67"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#784f0af919f467115774be372bf0dbd7"><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#3b05480e39db306e67fadbc79d394529"><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#82d810f9f90b79e8fe98d90a63070c32"><span class="id" title="notation">`</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#82d810f9f90b79e8fe98d90a63070c32"><span class="id" title="notation">_i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.vector.html#fb707feae4acc20b3f4404c2e515b2a1"><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#fb707feae4acc20b3f4404c2e515b2a1"><span class="id" title="notation">>></span></a>%<span class="id" title="var">VS</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Zchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/>
<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">phi</span> <span class="id" title="var">chi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#character"><span class="id" title="definition">character</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">chi</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.character.html#7d5ba9be6923d4bf4a568a8a939b7ab0"><span class="id" title="notation">_i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">chi1</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#chi1"><span class="id" title="variable">chi1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#character"><span class="id" title="definition">character</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">chi2</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#chi2"><span class="id" title="variable">chi2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.character.character.html#character"><span class="id" title="definition">character</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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#51dc792c356ca1a71a3094b50d6bb2fb"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#de3e30c288f66ee879ea2b40e81e186c"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#de3e30c288f66ee879ea2b40e81e186c"><span class="id" title="notation">sum_i</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a>.<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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span>, <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cint"><span class="id" title="definition">Cint</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="Cnat_cfnorm_vchar"><span class="id" title="lemma">Cnat_cfnorm_vchar</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span>, <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.field.algC.html#Algebraics.Exports.Cnat"><span class="id" title="definition">Cnat</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/>
<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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">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#2d0cfb150261028f4ebd2ba355623dcc"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/>
<br/>
<span class="id" title="keyword">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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<a name="VChar.CfdotPairwiseOrthogonal.nu"><span class="id" title="variable">nu</span></a> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#M"><span class="id" title="variable">M</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.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/V8.9.0/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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfdotPairwiseOrthogonal.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#0e493beb85c9c1b3ab2241ceeaa98b08"><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#0e493beb85c9c1b3ab2241ceeaa98b08"><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#0e493beb85c9c1b3ab2241ceeaa98b08"><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#3b05480e39db306e67fadbc79d394529"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><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#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#651a776cde67abfb8f7231c08f29d878"><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#651a776cde67abfb8f7231c08f29d878"><span class="id" title="notation">)^*</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><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#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">^+</span></a> 2 <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.vector.html#fb707feae4acc20b3f4404c2e515b2a1"><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#fb707feae4acc20b3f4404c2e515b2a1"><span class="id" title="notation">>></span></a>%<span class="id" title="var">VS</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#69c431a9c94f6f30a655bd7ddb59037b"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<a name="VChar.CfDotOrthonormal.nu"><span class="id" title="variable">nu</span></a> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#M"><span class="id" title="variable">M</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span>, <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#VChar.CfDotOrthonormal.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#651a776cde67abfb8f7231c08f29d878"><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#651a776cde67abfb8f7231c08f29d878"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><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#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><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#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">)%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a>.<br/>
<br/>
<span class="id" title="keyword">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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.vector.html#fb707feae4acc20b3f4404c2e515b2a1"><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#fb707feae4acc20b3f4404c2e515b2a1"><span class="id" title="notation">>></span></a>%<span class="id" title="var">VS</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">{</span></a><span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#3b05480e39db306e67fadbc79d394529"><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/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><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#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">)%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a>.<br/>
<br/>
<span class="id" title="keyword">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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a><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#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><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#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><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#c3ff8d84d4e3e273bebfcf7502deb41a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">b</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><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/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><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#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> 4)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">{</span></a><span class="id" title="var">S</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#c3913abe839346eb60d82da74b0b1f67"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#c3913abe839346eb60d82da74b0b1f67"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#VChar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">|</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><span class="id" title="notation">(</span></a><span class="id" title="var">xi</span> <a class="idref" href="mathcomp.algebra.ssralg.html#706f4f0208bba5d79e26d335c76ea034"><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#706f4f0208bba5d79e26d335c76ea034"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">}</span></a>.<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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 2<a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">i</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">j</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><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/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_j</span></a>.<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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>) (<a name="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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><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#b15d1bebaaff5b5ed693647b6d36f348"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b15d1bebaaff5b5ed693647b6d36f348"><span class="id" title="notation">additive</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b15d1bebaaff5b5ed693647b6d36f348"><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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">{</span></a><span class="id" title="var">tau</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b9a9030f88e15d1a3aacd4e8ec9a2391"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b9a9030f88e15d1a3aacd4e8ec9a2391"><span class="id" title="notation">linear</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b9a9030f88e15d1a3aacd4e8ec9a2391"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><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#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">to</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">}</span></a>.<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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><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#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><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#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">to</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">{</span></a><span class="id" title="var">tau</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b9a9030f88e15d1a3aacd4e8ec9a2391"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b9a9030f88e15d1a3aacd4e8ec9a2391"><span class="id" title="notation">linear</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.L"><span class="id" title="variable">L</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Isometries.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b9a9030f88e15d1a3aacd4e8ec9a2391"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <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/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><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#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">to</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.character.classfun.html#9e012b901a34756891cc773ca063f3a7"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">}</span></a>.<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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Isometries.S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <a class="idref" href="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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#d531732ed602c7af62b88c7cfce824e5"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#d531732ed602c7af62b88c7cfce824e5"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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#d531732ed602c7af62b88c7cfce824e5"><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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/>
<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> (<span class="id" title="var">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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<span class="id" title="var">phi</span> <span class="id" title="var">chi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#AutVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><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#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#651a776cde67abfb8f7231c08f29d878"><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#651a776cde67abfb8f7231c08f29d878"><span class="id" title="notation">)^*</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#AutVchar.u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#651a776cde67abfb8f7231c08f29d878"><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#651a776cde67abfb8f7231c08f29d878"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">u</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">u</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#AutVchar.u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">^</span></a><a class="idref" href="mathcomp.character.vcharacter.html#1dcc5e3b162744dbc296c5f466424c6d"><span class="id" title="notation">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#chi"><span class="id" title="variable">chi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">Res</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.character.classfun.html#99c53e21af8dfe7d98f8f1da9621ebb6"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">Ind</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#cd7dae4d94d0890c33d51d534038960d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><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#b24325f513e9801012e6322700f34266"><span class="id" title="notation">^*</span></a>)%<span class="id" title="var">CF</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#daf4f1487eeda5c7b4c53a78a01e8b57"><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#ca7f9c8131cd704a6703ad86f415c132"><span class="id" title="notation">^#</span></a><a class="idref" href="mathcomp.character.vcharacter.html#daf4f1487eeda5c7b4c53a78a01e8b57"><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#73516a680e9150542d49d1098b491775"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#73516a680e9150542d49d1098b491775"><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#73516a680e9150542d49d1098b491775"><span class="id" title="notation">with</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#73516a680e9150542d49d1098b491775"><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#73516a680e9150542d49d1098b491775"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">{</span></a><span class="id" title="var">K</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#MoreVchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.solvable.frobenius.html#6a02d4f0bf764b40a5c4d5e7c25f76d3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.solvable.frobenius.html#6a02d4f0bf764b40a5c4d5e7c25f76d3"><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#6a02d4f0bf764b40a5c4d5e7c25f76d3"><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#6a02d4f0bf764b40a5c4d5e7c25f76d3"><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#6a02d4f0bf764b40a5c4d5e7c25f76d3"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">}</span></a>.<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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a> := <br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">pred</span></a> <span class="id" title="var">f</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr"><span class="id" title="definition">irr</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><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#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">group</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#dd8cd2228f051940101d045bfdffe2d9"><span class="id" title="notation">}</span></a>).<br/>
<br/>
<span class="id" title="keyword">Fact</span> <a name="dirr_key"><span class="id" title="lemma">dirr_key</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/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/V8.9.0/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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><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#3b05480e39db306e67fadbc79d394529"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">b</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">i</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><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#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><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#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> -1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><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#df45e8c2e8370fd4f0f7c4fdaf208180"><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#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">)%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#cfAut"><span class="id" title="definition">cfAut</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) := (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><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/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) : <a 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/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><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/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><span class="id" title="notation">.2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><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#c385a484ee9d1b4e0615924561a9b75e"><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/V8.9.0/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/V8.9.0/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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a> := <br/>
<a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">(</span></a>-1<a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><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/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">i</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.character.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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><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#df45e8c2e8370fd4f0f7c4fdaf208180"><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#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">)%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <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#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">)%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a>.<br/>
<br/>
<span class="id" title="keyword">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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><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#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="dirr_inj"><span class="id" title="lemma">dirr_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> (@<a class="idref" href="mathcomp.character.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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <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/V8.9.0/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#17198bb01f8e546f36bb74df399b01c5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#17198bb01f8e546f36bb74df399b01c5"><span class="id" title="notation">pick</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#17198bb01f8e546f36bb74df399b01c5"><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#df45e8c2e8370fd4f0f7c4fdaf208180"><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#17198bb01f8e546f36bb74df399b01c5"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#J"><span class="id" title="variable">J</span></a>) :<br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">phi</span>: <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">)}</span></a> := <br/>
<a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) : <br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#dirr_constt"><span class="id" title="definition">dirr_constt</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<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#b9596739b058766532fc6517a36fef9f"><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#8d0566c961139ec21811f52ef0c317db"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">phi</span> : <a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) (<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/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation"><</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><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/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><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#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.gT"><span class="id" title="variable">gT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.character.html#irr_constt"><span class="id" title="definition">irr_constt</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi_i"><span class="id" title="variable">phi_i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_i</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.character.html#fc972dbc606652894cd5958d13eb0ca3"><span class="id" title="notation">chi_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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><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#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3b05480e39db306e67fadbc79d394529"><span class="id" title="notation">*:</span></a> <a class="idref" href="mathcomp.character.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="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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><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#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a> <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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) <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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">Z</span></a><a class="idref" href="mathcomp.character.vcharacter.html#ce9d55d0b57b155b5129cffe024a4445"><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#ce9d55d0b57b155b5129cffe024a4445"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.classfun.html#bb709747b2c5cc15f051ad5d56651c60"><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#bb709747b2c5cc15f051ad5d56651c60"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> (<a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> 4)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><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#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.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#b9596739b058766532fc6517a36fef9f"><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#8d0566c961139ec21811f52ef0c317db"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><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#b4ba9f64661118f4ed0bad900f98d2a2"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><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#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">CF</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#Norm1vchar.G"><span class="id" title="variable">G</span></a><a class="idref" href="mathcomp.character.classfun.html#5112e587c59fdaca05e10d1764f09c4c"><span class="id" title="notation">)</span></a>) :<br/>
<a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">'[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><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#b4ba9f64661118f4ed0bad900f98d2a2"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">,</span></a><br/>
<a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b4ba9f64661118f4ed0bad900f98d2a2"><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#b4ba9f64661118f4ed0bad900f98d2a2"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <br/>
<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><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#b9596739b058766532fc6517a36fef9f"><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#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a><br/>
<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><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#b9596739b058766532fc6517a36fef9f"><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#8d0566c961139ec21811f52ef0c317db"><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#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">%:</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#6411ed08724033ae48d2865f0380d533"><span class="id" title="notation">R</span></a>.<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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.character.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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">phi</span> <span class="id" title="var">psi</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.classfun.html#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.character.vcharacter.html#phi"><span class="id" title="variable">phi</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#c7f78cf1f6a5e4f664654f7d671ca752"><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#d6b5e89d170c69f67e0b52af88e95c1d"><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#d6b5e89d170c69f67e0b52af88e95c1d"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#psi"><span class="id" title="variable">psi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.character.vcharacter.html#phi1"><span class="id" title="variable">phi1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#f031fe1957c4a4a8e217aa46af2b4e25"><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/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><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/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><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/>
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