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diff --git a/docs/htmldoc/mathcomp.algebra.finalg.html b/docs/htmldoc/mathcomp.algebra.finalg.html deleted file mode 100644 index 53669ff..0000000 --- a/docs/htmldoc/mathcomp.algebra.finalg.html +++ /dev/null @@ -1,1691 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml"> -<head> -<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> -<link href="coqdoc.css" rel="stylesheet" type="text/css" /> -<title>mathcomp.algebra.finalg</title> -</head> - -<body> - -<div id="page"> - -<div id="header"> -</div> - -<div id="main"> - -<h1 class="libtitle">Library mathcomp.algebra.finalg</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 clones the entire ssralg hierachy for finite types; this allows - type inference to function properly on expressions that mix combinatorial - and algebraic operators (e.g., [set x + y | x in A, y in A]). - finZmodType, finRingType, finComRingType, finUnitRingType, - finComUnitRingType, finIdomType, finFieldType finLmodType, - finLalgType finAlgType finUnitAlgType - == the finite counterparts of zmodType, etc. - Note that a finFieldType is canonically decidable. All these structures - can be derived using [xxxType of T] forms, e.g., if R has both canonical - finType and ringType structures, then - Canonical R_finRingType := Eval hnf in [finRingType of R]. - declares the derived finRingType structure for R. As the implementation - of the derivation is somewhat involved, the Eval hnf normalization is - strongly recommended. - This file also provides direct tie-ins with finite group theory: - [baseFinGroupType of R for +%R] == the (canonical) additive group - [finGroupType of R for +%R] structures for R - {unit R} == the type of units of R, which has a - canonical group structure. - FinRing.unit R Ux == the element of {unit R} corresponding - to x, where Ux : x \in GRing.unit. - 'U%act == the action by right multiplication of - {unit R} on R, via FinRing.unit_act. - (This is also a group action.) -</div> -<div class="code"> - -<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">Set Implicit Arguments</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing"><span class="id" title="module">FinRing</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Generic"><span class="id" title="section">Generic</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Implicits -</div> -<div class="code"> -<span class="id" title="keyword">Variables</span> (<a name="FinRing.Generic.type"><span class="id" title="variable">type</span></a> <a name="FinRing.Generic.base_type"><span class="id" title="variable">base_type</span></a> : <span class="id" title="keyword">Type</span>) (<a name="FinRing.Generic.class_of"><span class="id" title="variable">class_of</span></a> <a name="FinRing.Generic.base_of"><span class="id" title="variable">base_of</span></a> : <span class="id" title="keyword">Type</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> <span class="id" title="keyword">Type</span>).<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Generic.to_choice"><span class="id" title="variable">to_choice</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">T</span>, <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.base_of"><span class="id" title="variable">base_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#Choice.class_of"><span class="id" title="record">Choice.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#T"><span class="id" title="variable">T</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Generic.base_sort"><span class="id" title="variable">base_sort</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.base_type"><span class="id" title="variable">base_type</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">Type</span>.<br/> - -<br/> -</div> - -<div class="doc"> - Explicits -</div> -<div class="code"> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Generic.Pack"><span class="id" title="variable">Pack</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">T</span>, <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.class_of"><span class="id" title="variable">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#T"><span class="id" title="variable">T</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.finalg.html#FinRing.Generic.type"><span class="id" title="variable">type</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Generic.Class"><span class="id" title="variable">Class</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">T</span> <span class="id" title="var">b</span>, <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#T"><span class="id" title="variable">T</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.to_choice"><span class="id" title="variable">to_choice</span></a> <a class="idref" href="mathcomp.algebra.finalg.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="mathcomp.algebra.finalg.html#FinRing.Generic.class_of"><span class="id" title="variable">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#T"><span class="id" title="variable">T</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Generic.base_class"><span class="id" title="variable">base_class</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">bT</span>, <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.base_of"><span class="id" title="variable">base_of</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.base_sort"><span class="id" title="variable">base_sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#bT"><span class="id" title="variable">bT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <span class="id" title="var">T</span> :=<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">bT</span> <span class="id" title="var">b</span> & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.base_class"><span class="id" title="variable">base_class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#bT"><span class="id" title="variable">bT</span></a>) <a class="idref" href="mathcomp.algebra.finalg.html#b"><span class="id" title="variable">b</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">fT</span> <span class="id" title="var">m</span> & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.class"><span class="id" title="definition">Finite.class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#fT"><span class="id" title="variable">fT</span></a>) (<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Class"><span class="id" title="constructor">Finite.Class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#m"><span class="id" title="variable">m</span></a>) ⇒<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.Pack"><span class="id" title="variable">Pack</span></a> (@<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic.Class"><span class="id" title="variable">Class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#m"><span class="id" title="variable">m</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Generic"><span class="id" title="section">Generic</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">GRing.Theory</span>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.groupMixin"><span class="id" title="definition">groupMixin</span></a> <span class="id" title="var">V</span> := <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Mixin"><span class="id" title="definition">FinGroup.Mixin</span></a> (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Theory.addrA"><span class="id" title="definition">addrA</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#V"><span class="id" title="variable">V</span></a>) (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Theory.add0r"><span class="id" title="definition">add0r</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#V"><span class="id" title="variable">V</span></a>) (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Theory.addNr"><span class="id" title="definition">addNr</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#V"><span class="id" title="variable">V</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Zmodule"><span class="id" title="module">Zmodule</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Zmodule.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.Zmodule.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">M</span> :=<br/> - <a name="FinRing.Zmodule.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.Zmodule.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.class_of"><span class="id" title="record">GRing.Zmodule.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>; <a name="FinRing.Zmodule.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.Zmodule.type"><span class="id" title="record">type</span></a> := <a name="FinRing.Zmodule.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.Zmodule.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Class"><span class="id" title="constructor">Class</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.class"><span class="id" title="definition">GRing.Zmodule.class</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.Zmodule.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.zmod_finType"><span class="id" title="definition">zmod_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.zmod_baseFinGroupType"><span class="id" title="definition">zmod_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.zmod_finGroupType"><span class="id" title="definition">zmod_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmod_baseFinGroupType"><span class="id" title="definition">zmod_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.countZmod_finType"><span class="id" title="definition">countZmod_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmodType"><span class="id" title="definition">countZmodType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.countZmod_baseFinGroupType"><span class="id" title="definition">countZmod_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Zmodule.countZmod_finGroupType"><span class="id" title="definition">countZmod_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmod_baseFinGroupType"><span class="id" title="definition">countZmod_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Zmodule.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base"><span class="id" title="projection">GRing.Zmodule.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.base2"><span class="id" title="definition">CountRing.Zmodule.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.mixin"><span class="id" title="projection">mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.mixin"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.mixin"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.mixin"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.mixin"><span class="id" title="projection">mixin_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmod_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmod_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmod_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmod_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmod_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmod_finGroupType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Zmodule.Exports.finZmodType"><span class="id" title="abbreviation">finZmodType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="144f70011c058d1c741eaa431b4b8944"><span class="id" title="notation">"</span></a>[ 'finZmodType' 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finZmodType' 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d6b25f501b9fb5e9b743073d52f24511"><span class="id" title="notation">"</span></a>[ 'baseFinGroupType' 'of' R 'for' +%R ]" :=<br/> - (<a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.BaseFinGroupType"><span class="id" title="abbreviation">BaseFinGroupType</span></a> <span class="id" title="var">R</span> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.groupMixin"><span class="id" title="definition">groupMixin</span></a> <span class="id" title="var">_</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'baseFinGroupType' 'of' R 'for' +%R ]")<br/> - : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a37f16a335f7a3ac65f83e3545c3e50c"><span class="id" title="notation">"</span></a>[ 'finGroupType' 'of' R 'for' +%R ]" :=<br/> - (@<a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.clone"><span class="id" title="definition">FinGroup.clone</span></a> <span class="id" title="var">R</span> <span class="id" title="var">_</span> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.finGroupType"><span class="id" title="definition">finGroupType</span></a> <span class="id" title="var">_</span>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finGroupType' 'of' R 'for' +%R ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule"><span class="id" title="module">Zmodule</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Zmodule.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.AdditiveGroup"><span class="id" title="section">AdditiveGroup</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.AdditiveGroup.U"><span class="id" title="variable">U</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.finZmodType"><span class="id" title="abbreviation">finZmodType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.AdditiveGroup.U"><span class="id" title="variable">U</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.zmod1gE"><span class="id" title="lemma">zmod1gE</span></a> : 1%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.AdditiveGroup.U"><span class="id" title="variable">U</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.zmodVgE"><span class="id" title="lemma">zmodVgE</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a>%<span class="id" title="var">g</span> <a class="idref" href="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.algebra.finalg.html#x"><span class="id" title="variable">x</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.zmodMgE"><span class="id" title="lemma">zmodMgE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : (<a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a>)%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.zmodXgE"><span class="id" title="lemma">zmodXgE</span></a> <span class="id" title="var">n</span> <span class="id" title="var">x</span> : (<a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#06cdd2633d7788bac7abeac13b2dd91e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#n"><span class="id" title="variable">n</span></a>)%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#e9001f602764f7896bb1eb34bf606a23"><span class="id" title="notation">*+</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#n"><span class="id" title="variable">n</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.zmod_mulgC"><span class="id" title="lemma">zmod_mulgC</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.fingroup.fingroup.html#commute"><span class="id" title="definition">commute</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.zmod_abelian"><span class="id" title="lemma">zmod_abelian</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.AdditiveGroup.U"><span class="id" title="variable">U</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.fingroup.fingroup.html#abelian"><span class="id" title="definition">abelian</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.AdditiveGroup"><span class="id" title="section">AdditiveGroup</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Ring"><span class="id" title="module">Ring</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Ring.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.Ring.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">R</span> :=<br/> - <a name="FinRing.Ring.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.Ring.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.class_of"><span class="id" title="record">GRing.Ring.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a>; <a name="FinRing.Ring.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.Ring.type"><span class="id" title="record">type</span></a> := <a name="FinRing.Ring.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.Ring.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Class"><span class="id" title="constructor">Class</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.class"><span class="id" title="definition">GRing.Ring.class</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.Ring.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.ring_finType"><span class="id" title="definition">ring_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">ringType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.ring_baseFinGroupType"><span class="id" title="definition">ring_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.ring_finGroupType"><span class="id" title="definition">ring_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ring_baseFinGroupType"><span class="id" title="definition">ring_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.ring_finZmodType"><span class="id" title="definition">ring_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.countRing_finType"><span class="id" title="definition">countRing_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">countRingType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.countRing_baseFinGroupType"><span class="id" title="definition">countRing_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.countRing_finGroupType"><span class="id" title="definition">countRing_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRing_baseFinGroupType"><span class="id" title="definition">countRing_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.countRing_finZmodType"><span class="id" title="definition">countRing_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Import</span> <a name="FinRing.Ring.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base"><span class="id" title="projection">GRing.Ring.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base2"><span class="id" title="definition">CountRing.Ring.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.base3"><span class="id" title="definition">Zmodule.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ring_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ring_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ring_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ring_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRing_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRing_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRing_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRing_finZmodType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Ring.Exports.finRingType"><span class="id" title="abbreviation">finRingType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="dfd62d789441026daed4d1ea30e2ff11"><span class="id" title="notation">"</span></a>[ 'finRingType' 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finRingType' 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Ring.Unit"><span class="id" title="section">Unit</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Ring.Unit.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.finRingType"><span class="id" title="abbreviation">finRingType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.is_inv"><span class="id" title="definition">is_inv</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Unit.R"><span class="id" title="variable">R</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.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 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> <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.algebra.finalg.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</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/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.unit"><span class="id" title="definition">unit</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#65c8f47ea0daafc83f7bb18bc9eca61f"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#65c8f47ea0daafc83f7bb18bc9eca61f"><span class="id" title="notation">qualify</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#65c8f47ea0daafc83f7bb18bc9eca61f"><span class="id" title="notation">a</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#65c8f47ea0daafc83f7bb18bc9eca61f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Unit.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#65c8f47ea0daafc83f7bb18bc9eca61f"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">∃</span></a> <span class="id" title="var">y</span><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.is_inv"><span class="id" title="definition">is_inv</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea6c97f834d69613538d4da1fb704b25"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#65c8f47ea0daafc83f7bb18bc9eca61f"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Ring.inv"><span class="id" title="definition">inv</span></a> <span class="id" title="var">x</span> := <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.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#pick"><span class="id" title="definition">pick</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.is_inv"><span class="id" title="definition">is_inv</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a>)).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.Ring.mulVr"><span class="id" title="lemma">mulVr</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.algebra.finalg.html#FinRing.Ring.unit"><span class="id" title="definition">unit</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#left_inverse"><span class="id" title="definition">left_inverse</span></a> 1 <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.inv"><span class="id" title="definition">inv</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">R</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="FinRing.Ring.mulrV"><span class="id" title="lemma">mulrV</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.algebra.finalg.html#FinRing.Ring.unit"><span class="id" title="definition">unit</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#right_inverse"><span class="id" title="definition">right_inverse</span></a> 1 <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.inv"><span class="id" title="definition">inv</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">R</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="FinRing.Ring.intro_unit"><span class="id" title="lemma">intro_unit</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 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.algebra.finalg.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#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.algebra.finalg.html#FinRing.Ring.unit"><span class="id" title="definition">unit</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.Ring.invr_out"><span class="id" title="lemma">invr_out</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#790b887fcb3f1d578b2c7a5460f7aeb5"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#790b887fcb3f1d578b2c7a5460f7aeb5"><span class="id" title="notation">predC</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.unit"><span class="id" title="definition">unit</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#790b887fcb3f1d578b2c7a5460f7aeb5"><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="mathcomp.algebra.finalg.html#FinRing.Ring.inv"><span class="id" title="definition">inv</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</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">Definition</span> <a name="FinRing.Ring.UnitMixin"><span class="id" title="definition">UnitMixin</span></a> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Mixin"><span class="id" title="constructor">GRing.UnitRing.Mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.mulVr"><span class="id" title="lemma">mulVr</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.mulrV"><span class="id" title="lemma">mulrV</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.intro_unit"><span class="id" title="lemma">intro_unit</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.invr_out"><span class="id" title="lemma">invr_out</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Unit"><span class="id" title="section">Unit</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring"><span class="id" title="module">Ring</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Ring.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.ComRing"><span class="id" title="module">ComRing</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.ComRing.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.ComRing.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">R</span> :=<br/> - <a name="FinRing.ComRing.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.ComRing.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.class_of"><span class="id" title="record">GRing.ComRing.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a>; <a name="FinRing.ComRing.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.ComRing.type"><span class="id" title="record">type</span></a> := <a name="FinRing.ComRing.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.ComRing.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Class"><span class="id" title="constructor">Class</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.class"><span class="id" title="definition">GRing.ComRing.class</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.ComRing.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.comRingType"><span class="id" title="definition">comRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Pack"><span class="id" title="constructor">GRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.ComRing.Pack"><span class="id" title="constructor">CountRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.comRing_finType"><span class="id" title="definition">comRing_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">comRingType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.comRing_baseFinGroupType"><span class="id" title="definition">comRing_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.comRing_finGroupType"><span class="id" title="definition">comRing_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRing_baseFinGroupType"><span class="id" title="definition">comRing_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.comRing_finZmodType"><span class="id" title="definition">comRing_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.comRing_finRingType"><span class="id" title="definition">comRing_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countComRing_finType"><span class="id" title="definition">countComRing_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countComRing_baseFinGroupType"><span class="id" title="definition">countComRing_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countComRing_finGroupType"><span class="id" title="definition">countComRing_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRing_baseFinGroupType"><span class="id" title="definition">countComRing_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countComRing_finZmodType"><span class="id" title="definition">countComRing_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComRing.countComRing_finRingType"><span class="id" title="definition">countComRing_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.ComRing.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base"><span class="id" title="projection">GRing.ComRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base2"><span class="id" title="definition">CountRing.ComRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.base3"><span class="id" title="definition">Ring.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.comRingType"><span class="id" title="definition">GRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.countComRingType"><span class="id" title="definition">CountRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRing_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRing_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRing_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRing_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRing_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRing_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRing_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRing_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRing_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRing_finRingType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.ComRing.Exports.finComRingType"><span class="id" title="abbreviation">finComRingType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.type"><span class="id" title="record">FinRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="b13c97e55bebdc1c181a99b80106c099"><span class="id" title="notation">"</span></a>[ 'finComRingType' 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finComRingType' 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing"><span class="id" title="module">ComRing</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">ComRing.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.UnitRing"><span class="id" title="module">UnitRing</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.UnitRing.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.UnitRing.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">R</span> :=<br/> - <a name="FinRing.UnitRing.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.UnitRing.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.class_of"><span class="id" title="record">GRing.UnitRing.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a>; <a name="FinRing.UnitRing.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.UnitRing.type"><span class="id" title="record">type</span></a> := <a name="FinRing.UnitRing.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.UnitRing.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Class"><span class="id" title="constructor">Class</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.class"><span class="id" title="definition">GRing.UnitRing.class</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.UnitRing.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Pack"><span class="id" title="constructor">GRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.UnitRing.Pack"><span class="id" title="constructor">CountRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.unitRing_finType"><span class="id" title="definition">unitRing_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.unitRing_baseFinGroupType"><span class="id" title="definition">unitRing_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.unitRing_finGroupType"><span class="id" title="definition">unitRing_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRing_baseFinGroupType"><span class="id" title="definition">unitRing_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.unitRing_finZmodType"><span class="id" title="definition">unitRing_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.unitRing_finRingType"><span class="id" title="definition">unitRing_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countUnitRing_finType"><span class="id" title="definition">countUnitRing_finType</span></a> :=<br/> - @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countUnitRing_baseFinGroupType"><span class="id" title="definition">countUnitRing_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countUnitRing_finGroupType"><span class="id" title="definition">countUnitRing_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRing_baseFinGroupType"><span class="id" title="definition">countUnitRing_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countUnitRing_finZmodType"><span class="id" title="definition">countUnitRing_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitRing.countUnitRing_finRingType"><span class="id" title="definition">countUnitRing_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.UnitRing.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base"><span class="id" title="projection">GRing.UnitRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base2"><span class="id" title="definition">CountRing.UnitRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.base3"><span class="id" title="definition">Ring.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.unitRingType"><span class="id" title="definition">GRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.countUnitRingType"><span class="id" title="definition">CountRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finRingType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.UnitRing.Exports.finUnitRingType"><span class="id" title="abbreviation">finUnitRingType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.type"><span class="id" title="record">FinRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="157b0761db3726d8e1bc0a71108dc48f"><span class="id" title="notation">"</span></a>[ 'finUnitRingType' 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finUnitRingType' 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing"><span class="id" title="module">UnitRing</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">UnitRing.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.UnitsGroup"><span class="id" title="section">UnitsGroup</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.UnitsGroup.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.finUnitRingType"><span class="id" title="abbreviation">finUnitRingType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Inductive</span> <a name="FinRing.unit_of"><span class="id" title="inductive">unit_of</span></a> (<span class="id" title="var">phR</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup.R"><span class="id" title="variable">R</span></a>) := <a name="FinRing.Unit"><span class="id" title="constructor">Unit</span></a> (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup.R"><span class="id" title="variable">R</span></a>) <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.algebra.finalg.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#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.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.UnitsGroup.phR"><span class="id" title="variable">phR</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup.R"><span class="id" title="variable">R</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.uval"><span class="id" title="definition">uval</span></a> <span class="id" title="var">u</span> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Unit"><span class="id" title="constructor">Unit</span></a> <span class="id" title="var">x</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">x</span>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_subType</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#c2d02b544d823cdc1e1e08de552cdba4"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#c2d02b544d823cdc1e1e08de552cdba4"><span class="id" title="notation">subType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c2d02b544d823cdc1e1e08de552cdba4"><span class="id" title="notation">for</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uval"><span class="id" title="definition">uval</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#c2d02b544d823cdc1e1e08de552cdba4"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.unit_eqMixin"><span class="id" title="definition">unit_eqMixin</span></a> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">eqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_eqType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.EqType"><span class="id" title="abbreviation">EqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_eqMixin"><span class="id" title="definition">unit_eqMixin</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.unit_choiceMixin"><span class="id" title="definition">unit_choiceMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">choiceMixin</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_choiceType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Exports.ChoiceType"><span class="id" title="abbreviation">ChoiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_choiceMixin"><span class="id" title="definition">unit_choiceMixin</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.unit_countMixin"><span class="id" title="definition">unit_countMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">countMixin</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_countType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Exports.CountType"><span class="id" title="abbreviation">CountType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_countMixin"><span class="id" title="definition">unit_countMixin</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_subCountType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">subCountType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.unit_finMixin"><span class="id" title="definition">unit_finMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">finMixin</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_finType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.FinType"><span class="id" title="abbreviation">FinType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_finMixin"><span class="id" title="definition">unit_finMixin</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_subFinType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">subFinType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.unit1"><span class="id" title="definition">unit1</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Unit"><span class="id" title="constructor">Unit</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup.phR"><span class="id" title="variable">phR</span></a> (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.unitr1"><span class="id" title="lemma">GRing.unitr1</span></a> <span class="id" title="var">_</span>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.unit_inv_proof"><span class="id" title="lemma">unit_inv_proof</span></a> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">)^-1</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.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</span></a>.<br/> - <span class="id" title="keyword">Definition</span> <a name="FinRing.unit_inv"><span class="id" title="definition">unit_inv</span></a> <span class="id" title="var">u</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Unit"><span class="id" title="constructor">Unit</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup.phR"><span class="id" title="variable">phR</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_inv_proof"><span class="id" title="lemma">unit_inv_proof</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.unit_mul_proof"><span class="id" title="lemma">unit_mul_proof</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.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#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.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</span></a>.<br/> - <span class="id" title="keyword">Definition</span> <a name="FinRing.unit_mul"><span class="id" title="definition">unit_mul</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Unit"><span class="id" title="constructor">Unit</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup.phR"><span class="id" title="variable">phR</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_mul_proof"><span class="id" title="lemma">unit_mul_proof</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#v"><span class="id" title="variable">v</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.unit_muluA"><span class="id" title="lemma">unit_muluA</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#associative"><span class="id" title="definition">associative</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_mul"><span class="id" title="definition">unit_mul</span></a>.<br/> - <span class="id" title="keyword">Lemma</span> <a name="FinRing.unit_mul1u"><span class="id" title="lemma">unit_mul1u</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit1"><span class="id" title="definition">unit1</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_mul"><span class="id" title="definition">unit_mul</span></a>.<br/> - <span class="id" title="keyword">Lemma</span> <a name="FinRing.unit_mulVu"><span class="id" title="lemma">unit_mulVu</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_inverse"><span class="id" title="definition">left_inverse</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit1"><span class="id" title="definition">unit1</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_inv"><span class="id" title="definition">unit_inv</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_mul"><span class="id" title="definition">unit_mul</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.unit_GroupMixin"><span class="id" title="definition">unit_GroupMixin</span></a> := <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Mixin"><span class="id" title="definition">FinGroup.Mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_muluA"><span class="id" title="lemma">unit_muluA</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_mul1u"><span class="id" title="lemma">unit_mul1u</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_mulVu"><span class="id" title="lemma">unit_mulVu</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_baseFinGroupType</span> :=<br/> - <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.BaseFinGroupType"><span class="id" title="abbreviation">BaseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_GroupMixin"><span class="id" title="definition">unit_GroupMixin</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_finGroupType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.fingroup.fingroup.html#FinGroup.Exports.FinGroupType"><span class="id" title="abbreviation">FinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_mulVu"><span class="id" title="lemma">unit_mulVu</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.val_unit1"><span class="id" title="lemma">val_unit1</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</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.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</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/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.val_unitM"><span class="id" title="lemma">val_unitM</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#8b8794efbfbae1b793d9cb62ce802285"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a>)%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#y"><span class="id" title="variable">y</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.val_unitV"><span class="id" title="lemma">val_unitV</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.fingroup.fingroup.html#766fd55608aa0e125ed6f55c83bcc09a"><span class="id" title="notation">^-1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a>)%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">)^-1</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.val_unitX"><span class="id" title="lemma">val_unitX</span></a> <span class="id" title="var">n</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.fingroup.fingroup.html#06cdd2633d7788bac7abeac13b2dd91e"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.algebra.finalg.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.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.uT"><span class="id" title="abbreviation">uT</span></a>)%<span class="id" title="var">g</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#663140372ac3b275aae871b74b140513"><span class="id" title="notation">^+</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#n"><span class="id" title="variable">n</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.unit_act"><span class="id" title="definition">unit_act</span></a> <span class="id" title="var">x</span> <span class="id" title="var">u</span> := <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.unit_actE"><span class="id" title="lemma">unit_actE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_act"><span class="id" title="definition">unit_act</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#u"><span class="id" title="variable">u</span></a>. <br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_action</span> :=<br/> - @<a class="idref" href="mathcomp.fingroup.action.html#TotalAction"><span class="id" title="definition">TotalAction</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_act"><span class="id" title="definition">unit_act</span></a> (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.mulr1"><span class="id" title="lemma">GRing.mulr1</span></a> <span class="id" title="var">_</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.mulrA"><span class="id" title="lemma">GRing.mulrA</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.unit_is_groupAction"><span class="id" title="lemma">unit_is_groupAction</span></a> : @<a class="idref" href="mathcomp.fingroup.action.html#is_groupAction"><span class="id" title="definition">is_groupAction</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_action"><span class="id" title="definition">unit_action</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_groupAction</span> := <a class="idref" href="mathcomp.fingroup.action.html#GroupAction"><span class="id" title="constructor">GroupAction</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_is_groupAction"><span class="id" title="lemma">unit_is_groupAction</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroup"><span class="id" title="section">UnitsGroup</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Import</span> <a name="FinRing.UnitsGroupExports"><span class="id" title="module">UnitsGroupExports</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_subType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_eqType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_choiceType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_countType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_subCountType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_subFinType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_action</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_groupAction</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitsGroupExports"><span class="id" title="module">UnitsGroupExports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.unit"><span class="id" title="abbreviation">unit</span></a> <span class="id" title="var">R</span> <span class="id" title="var">Ux</span> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Unit"><span class="id" title="constructor">Unit</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>) <span class="id" title="var">Ux</span>).<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.ComUnitRing"><span class="id" title="module">ComUnitRing</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.ComUnitRing.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.ComUnitRing.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">R</span> :=<br/> - <a name="FinRing.ComUnitRing.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.ComUnitRing.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComUnitRing.class_of"><span class="id" title="record">GRing.ComUnitRing.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a>; <a name="FinRing.ComUnitRing.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.ComUnitRing.type"><span class="id" title="record">type</span></a> := <a name="FinRing.ComUnitRing.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.ComUnitRing.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Class"><span class="id" title="constructor">Class</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComUnitRing.class"><span class="id" title="definition">GRing.ComUnitRing.class</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.ComUnitRing.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comRingType"><span class="id" title="definition">comRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Pack"><span class="id" title="constructor">GRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.ComRing.Pack"><span class="id" title="constructor">CountRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.finComRingType"><span class="id" title="definition">finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Pack"><span class="id" title="constructor">GRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.UnitRing.Pack"><span class="id" title="constructor">CountRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComUnitRing.Pack"><span class="id" title="constructor">GRing.ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.ComUnitRing.Pack"><span class="id" title="constructor">CountRing.ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRing_finType"><span class="id" title="definition">comUnitRing_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRing_baseFinGroupType"><span class="id" title="definition">comUnitRing_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRing_finGroupType"><span class="id" title="definition">comUnitRing_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRing_baseFinGroupType"><span class="id" title="definition">comUnitRing_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRing_finZmodType"><span class="id" title="definition">comUnitRing_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRing_finRingType"><span class="id" title="definition">comUnitRing_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRing_finComRingType"><span class="id" title="definition">comUnitRing_finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comUnitRing_finUnitRingType"><span class="id" title="definition">comUnitRing_finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRing_finType"><span class="id" title="definition">countComUnitRing_finType</span></a> :=<br/> - @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRing_baseFinGroupType"><span class="id" title="definition">countComUnitRing_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRing_finGroupType"><span class="id" title="definition">countComUnitRing_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRing_baseFinGroupType"><span class="id" title="definition">countComUnitRing_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRing_finZmodType"><span class="id" title="definition">countComUnitRing_finZmodType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRing_finRingType"><span class="id" title="definition">countComUnitRing_finRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRing_finComRingType"><span class="id" title="definition">countComUnitRing_finComRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComUnitRing_finUnitRingType"><span class="id" title="definition">countComUnitRing_finUnitRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.unitRing_finComRingType"><span class="id" title="definition">unitRing_finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countUnitRing_finComRingType"><span class="id" title="definition">countUnitRing_finComRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.comRing_finUnitRingType"><span class="id" title="definition">comRing_finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.countComRing_finUnitRingType"><span class="id" title="definition">countComRing_finUnitRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.ComUnitRing.finComRing_finUnitRingType"><span class="id" title="definition">finComRing_finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finComRingType"><span class="id" title="definition">finComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.ComUnitRing.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base"><span class="id" title="projection">GRing.ComUnitRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base2"><span class="id" title="definition">CountRing.ComUnitRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base3"><span class="id" title="definition">ComRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base4"><span class="id" title="definition">base4</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base4"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base4"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base4"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.base4"><span class="id" title="definition">UnitRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comRingType"><span class="id" title="definition">GRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComRingType"><span class="id" title="definition">CountRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finComRingType"><span class="id" title="definition">finComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finComRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finComRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finComRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finComRingType"><span class="id" title="definition">ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.unitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.unitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.unitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.unitRingType"><span class="id" title="definition">GRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countUnitRingType"><span class="id" title="definition">CountRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.finUnitRingType"><span class="id" title="definition">UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.comUnitRingType"><span class="id" title="definition">GRing.ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.countComUnitRingType"><span class="id" title="definition">CountRing.ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRing_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRing_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRing_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRing_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRing_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRing_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRing_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRing_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRing_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRing_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRing_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRing_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRing_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRing_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRing_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRing_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComRing_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.ComUnitRing.Exports.finComUnitRingType"><span class="id" title="abbreviation">finComUnitRingType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.type"><span class="id" title="record">FinRing.ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="29c2dac4b2cace3201f3f23b551d143a"><span class="id" title="notation">"</span></a>[ 'finComUnitRingType' 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finComUnitRingType' 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing"><span class="id" title="module">ComUnitRing</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">ComUnitRing.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.IntegralDomain"><span class="id" title="module">IntegralDomain</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.IntegralDomain.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.IntegralDomain.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">R</span> :=<br/> - <a name="FinRing.IntegralDomain.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.IntegralDomain.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.IntegralDomain.class_of"><span class="id" title="record">GRing.IntegralDomain.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a>; <a name="FinRing.IntegralDomain.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.IntegralDomain.type"><span class="id" title="record">type</span></a> := <a name="FinRing.IntegralDomain.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.IntegralDomain.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Class"><span class="id" title="constructor">Class</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.IntegralDomain.class"><span class="id" title="definition">GRing.IntegralDomain.class</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.IntegralDomain.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.comRingType"><span class="id" title="definition">comRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Pack"><span class="id" title="constructor">GRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countComRingType"><span class="id" title="definition">countComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.ComRing.Pack"><span class="id" title="constructor">CountRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.finComRingType"><span class="id" title="definition">finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.unitRingType"><span class="id" title="definition">unitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Pack"><span class="id" title="constructor">GRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.UnitRing.Pack"><span class="id" title="constructor">CountRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComUnitRing.Pack"><span class="id" title="constructor">GRing.ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.ComUnitRing.Pack"><span class="id" title="constructor">CountRing.ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.finComUnitRingType"><span class="id" title="definition">finComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.IntegralDomain.Pack"><span class="id" title="constructor">GRing.IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.IntegralDomain.Pack"><span class="id" title="constructor">CountRing.IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_finType"><span class="id" title="definition">idomain_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_baseFinGroupType"><span class="id" title="definition">idomain_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_finGroupType"><span class="id" title="definition">idomain_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomain_baseFinGroupType"><span class="id" title="definition">idomain_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_finZmodType"><span class="id" title="definition">idomain_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_finRingType"><span class="id" title="definition">idomain_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_finUnitRingType"><span class="id" title="definition">idomain_finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_finComRingType"><span class="id" title="definition">idomain_finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.idomain_finComUnitRingType"><span class="id" title="definition">idomain_finComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_finType"><span class="id" title="definition">countIdomain_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_baseFinGroupType"><span class="id" title="definition">countIdomain_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_finGroupType"><span class="id" title="definition">countIdomain_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomain_baseFinGroupType"><span class="id" title="definition">countIdomain_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_finZmodType"><span class="id" title="definition">countIdomain_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_finRingType"><span class="id" title="definition">countIdomain_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_finUnitRingType"><span class="id" title="definition">countIdomain_finUnitRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_finComRingType"><span class="id" title="definition">countIdomain_finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.IntegralDomain.countIdomain_finComUnitRingType"><span class="id" title="definition">countIdomain_finComUnitRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.IntegralDomain.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base"><span class="id" title="projection">GRing.IntegralDomain.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base2"><span class="id" title="definition">CountRing.IntegralDomain.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.base3"><span class="id" title="definition">ComUnitRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comRingType"><span class="id" title="definition">GRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComRingType"><span class="id" title="definition">CountRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComRingType"><span class="id" title="definition">finComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComRingType"><span class="id" title="definition">ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.unitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.unitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.unitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.unitRingType"><span class="id" title="definition">GRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countUnitRingType"><span class="id" title="definition">CountRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finUnitRingType"><span class="id" title="definition">UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.comUnitRingType"><span class="id" title="definition">GRing.ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countComUnitRingType"><span class="id" title="definition">CountRing.ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComUnitRingType"><span class="id" title="definition">finComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.finComUnitRingType"><span class="id" title="definition">ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.idomainType"><span class="id" title="definition">GRing.IntegralDomain.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomainType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.countIdomainType"><span class="id" title="definition">CountRing.IntegralDomain.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomainType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomain_finComUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomain_finComUnitRingType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.IntegralDomain.Exports.finIdomainType"><span class="id" title="abbreviation">finIdomainType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.type"><span class="id" title="record">FinRing.IntegralDomain.type</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="762465ada9848b70124d860dd97a755c"><span class="id" title="notation">"</span></a>[ 'finIdomainType' 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finIdomainType' 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain"><span class="id" title="module">IntegralDomain</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">IntegralDomain.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Field"><span class="id" title="module">Field</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Field.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.Field.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">R</span> :=<br/> - <a name="FinRing.Field.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.Field.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Field.class_of"><span class="id" title="record">GRing.Field.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a>; <a name="FinRing.Field.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.Field.type"><span class="id" title="record">type</span></a> := <a name="FinRing.Field.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.Field.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.Class"><span class="id" title="constructor">Class</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Field.class"><span class="id" title="definition">GRing.Field.class</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.type"><span class="id" title="record">type</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.Field.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.comRingType"><span class="id" title="definition">comRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Pack"><span class="id" title="constructor">GRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countComRingType"><span class="id" title="definition">countComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.ComRing.Pack"><span class="id" title="constructor">CountRing.ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finComRingType"><span class="id" title="definition">finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.unitRingType"><span class="id" title="definition">unitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Pack"><span class="id" title="constructor">GRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.UnitRing.Pack"><span class="id" title="constructor">CountRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComUnitRing.Pack"><span class="id" title="constructor">GRing.ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.ComUnitRing.Pack"><span class="id" title="constructor">CountRing.ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finComUnitRingType"><span class="id" title="definition">finComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.idomainType"><span class="id" title="definition">idomainType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.IntegralDomain.Pack"><span class="id" title="constructor">GRing.IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.IntegralDomain.Pack"><span class="id" title="constructor">CountRing.IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finIdomainType"><span class="id" title="definition">finIdomainType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Pack"><span class="id" title="constructor">IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Field.Pack"><span class="id" title="constructor">GRing.Field.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Field.Pack"><span class="id" title="constructor">CountRing.Field.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finType"><span class="id" title="definition">field_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_baseFinGroupType"><span class="id" title="definition">field_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finGroupType"><span class="id" title="definition">field_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.field_baseFinGroupType"><span class="id" title="definition">field_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finZmodType"><span class="id" title="definition">field_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finRingType"><span class="id" title="definition">field_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finUnitRingType"><span class="id" title="definition">field_finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finComRingType"><span class="id" title="definition">field_finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finComUnitRingType"><span class="id" title="definition">field_finComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.field_finIdomainType"><span class="id" title="definition">field_finIdomainType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Pack"><span class="id" title="constructor">IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finType"><span class="id" title="definition">countField_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_baseFinGroupType"><span class="id" title="definition">countField_baseFinGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finGroupType"><span class="id" title="definition">countField_finGroupType</span></a> :=<br/> - <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countField_baseFinGroupType"><span class="id" title="definition">countField_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finZmodType"><span class="id" title="definition">countField_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finRingType"><span class="id" title="definition">countField_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finUnitRingType"><span class="id" title="definition">countField_finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finComRingType"><span class="id" title="definition">countField_finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finComUnitRingType"><span class="id" title="definition">countField_finComUnitRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Field.countField_finIdomainType"><span class="id" title="definition">countField_finIdomainType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Pack"><span class="id" title="constructor">IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Field.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base"><span class="id" title="projection">GRing.Field.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base2"><span class="id" title="definition">CountRing.Field.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.base3"><span class="id" title="definition">IntegralDomain.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comRingType"><span class="id" title="definition">comRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comRingType"><span class="id" title="definition">GRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComRingType"><span class="id" title="definition">countComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComRingType"><span class="id" title="definition">CountRing.ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComRingType"><span class="id" title="definition">finComRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComRingType"><span class="id" title="definition">ComRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.unitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.unitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.unitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.unitRingType"><span class="id" title="definition">GRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countUnitRingType"><span class="id" title="definition">CountRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finUnitRingType"><span class="id" title="definition">UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comUnitRingType"><span class="id" title="definition">comUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.comUnitRingType"><span class="id" title="definition">GRing.ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">comUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComUnitRingType"><span class="id" title="definition">countComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countComUnitRingType"><span class="id" title="definition">CountRing.ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countComUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComUnitRingType"><span class="id" title="definition">finComUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finComUnitRingType"><span class="id" title="definition">ComUnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.idomainType"><span class="id" title="definition">idomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.idomainType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.idomainType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.idomainType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.idomainType"><span class="id" title="definition">GRing.IntegralDomain.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">idomainType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countIdomainType"><span class="id" title="definition">countIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countIdomainType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countIdomainType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countIdomainType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countIdomainType"><span class="id" title="definition">CountRing.IntegralDomain.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countIdomainType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finIdomainType"><span class="id" title="definition">finIdomainType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finIdomainType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finIdomainType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finIdomainType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.finIdomainType"><span class="id" title="definition">IntegralDomain.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finIdomainType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">fieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.fieldType"><span class="id" title="definition">GRing.Field.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">fieldType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">countFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.countFieldType"><span class="id" title="definition">CountRing.Field.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countFieldType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finComUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">field_finIdomainType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finComUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countField_finIdomainType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Field.Exports.finFieldType"><span class="id" title="abbreviation">finFieldType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.type"><span class="id" title="record">FinRing.Field.type</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="85a9f33cca8b2a31e30517c43d5ecb47"><span class="id" title="notation">"</span></a>[ 'finFieldType' 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finFieldType' 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field"><span class="id" title="module">Field</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Field.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.DecideField"><span class="id" title="section">DecideField</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.DecideField.F"><span class="id" title="variable">F</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.type"><span class="id" title="record">Field.type</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Fixpoint</span> <a name="FinRing.sat"><span class="id" title="definition">sat</span></a> <span class="id" title="var">e</span> <span class="id" title="var">f</span> :=<br/> - <span class="id" title="keyword">match</span> <a class="idref" href="mathcomp.algebra.finalg.html#f"><span class="id" title="variable">f</span></a> <span class="id" title="keyword">with</span><br/> - | <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Bool"><span class="id" title="constructor">GRing.Bool</span></a> <span class="id" title="var">b</span> ⇒ <span class="id" title="var">b</span><br/> - | <span class="id" title="var">t1</span> <a class="idref" href="mathcomp.algebra.ssralg.html#8ba71119b4b4369b5eb5b6037f9b1b72"><span class="id" title="notation">==</span></a> <span class="id" title="var">t2</span> ⇒ (<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.eval"><span class="id" title="definition">GRing.eval</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">t1</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.eval"><span class="id" title="definition">GRing.eval</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">t2</span>)%<span class="id" title="var">bool</span><br/> - | <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Unit"><span class="id" title="constructor">GRing.Unit</span></a> <span class="id" title="var">t</span> ⇒ <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.eval"><span class="id" title="definition">GRing.eval</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">t</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">is</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#f6c65697fefaf4504de1d4d641cd4409"><span class="id" title="notation">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</span></a><br/> - | <span class="id" title="var">f1</span> <a class="idref" href="mathcomp.algebra.ssralg.html#5a500d4ce4c6eea4df7cd2e3cacc0360"><span class="id" title="notation">∧</span></a> <span class="id" title="var">f2</span> ⇒ <a class="idref" href="mathcomp.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">f1</span> <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.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">f2</span><br/> - | <span class="id" title="var">f1</span> <a class="idref" href="mathcomp.algebra.ssralg.html#fb8e71b0a04b4fb792321652d3394589"><span class="id" title="notation">∨</span></a> <span class="id" title="var">f2</span> ⇒ <a class="idref" href="mathcomp.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">f1</span> <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.finalg.html#sat"><span class="id" title="definition">sat</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">f2</span><br/> - | <span class="id" title="var">f1</span> <a class="idref" href="mathcomp.algebra.ssralg.html#b7075a427ea950c442d03d47d831421c"><span class="id" title="notation">==></span></a> <span class="id" title="var">f2</span> ⇒ (<a class="idref" href="mathcomp.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">f1</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#a133e82bab56729f895f9b2b31e837cd"><span class="id" title="notation">==></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">f2</span>)%<span class="id" title="var">bool</span><br/> - | <a class="idref" href="mathcomp.algebra.ssralg.html#5a358d3997cc6f2a7919089a2f91e45f"><span class="id" title="notation">¬</span></a> <span class="id" title="var">f1</span> ⇒ <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.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">f1</span><br/> - | (<a class="idref" href="mathcomp.algebra.ssralg.html#ed4038db2198f4fe9955121b51cc9a06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#ed4038db2198f4fe9955121b51cc9a06"><span class="id" title="notation">∃</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#ed4038db2198f4fe9955121b51cc9a06"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#ed4038db2198f4fe9955121b51cc9a06"><span class="id" title="notation">X_k</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#ed4038db2198f4fe9955121b51cc9a06"><span class="id" title="notation">,</span></a> <span class="id" title="var">f1</span>) ⇒ <a class="idref" href="mathcomp.ssreflect.fintype.html#9b7547477b3531f14d89d6b13ad78482"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9b7547477b3531f14d89d6b13ad78482"><span class="id" title="notation">∃</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#9b7547477b3531f14d89d6b13ad78482"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecideField.F"><span class="id" title="variable">F</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#set_nth"><span class="id" title="definition">set_nth</span></a> 0%<span class="id" title="var">R</span> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">k</span> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a>) <span class="id" title="var">f1</span><a class="idref" href="mathcomp.ssreflect.fintype.html#9b7547477b3531f14d89d6b13ad78482"><span class="id" title="notation">]</span></a><br/> - | (<a class="idref" href="mathcomp.algebra.ssralg.html#61e99859b5405813120fb72b6bd3697e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#61e99859b5405813120fb72b6bd3697e"><span class="id" title="notation">∀</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#61e99859b5405813120fb72b6bd3697e"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#61e99859b5405813120fb72b6bd3697e"><span class="id" title="notation">X_k</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#61e99859b5405813120fb72b6bd3697e"><span class="id" title="notation">,</span></a> <span class="id" title="var">f1</span>) ⇒ <a class="idref" href="mathcomp.ssreflect.fintype.html#fb0199913c9911d56fa87965a9a828a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#fb0199913c9911d56fa87965a9a828a3"><span class="id" title="notation">∀</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#fb0199913c9911d56fa87965a9a828a3"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecideField.F"><span class="id" title="variable">F</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sat"><span class="id" title="definition">sat</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#set_nth"><span class="id" title="definition">set_nth</span></a> 0%<span class="id" title="var">R</span> <a class="idref" href="mathcomp.algebra.finalg.html#e"><span class="id" title="variable">e</span></a> <span class="id" title="var">k</span> <a class="idref" href="mathcomp.algebra.finalg.html#x"><span class="id" title="variable">x</span></a>) <span class="id" title="var">f1</span><a class="idref" href="mathcomp.ssreflect.fintype.html#fb0199913c9911d56fa87965a9a828a3"><span class="id" title="notation">]</span></a><br/> - <span class="id" title="keyword">end</span>%<span class="id" title="var">T</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="FinRing.decidable"><span class="id" title="lemma">decidable</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.DecidableField.axiom"><span class="id" title="definition">GRing.DecidableField.axiom</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.sat"><span class="id" title="definition">sat</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecidableFieldMixin"><span class="id" title="definition">DecidableFieldMixin</span></a> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.DecidableField.Exports.DecFieldMixin"><span class="id" title="abbreviation">DecFieldMixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.decidable"><span class="id" title="lemma">decidable</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecideField"><span class="id" title="section">DecideField</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.DecField"><span class="id" title="module">DecField</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.DecField.Joins"><span class="id" title="section">Joins</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.DecField.Joins.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.type"><span class="id" title="record">Field.type</span></a>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.DecField.Joins.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.Pack"><span class="id" title="constructor">Field.Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.class_of"><span class="id" title="record">Field.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xT"><span class="id" title="variable">xT</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Field.class"><span class="id" title="definition">Field.class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.cT"><span class="id" title="variable">cT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.type"><span class="id" title="definition">type</span></a> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.DecidableField.Exports.DecFieldType"><span class="id" title="abbreviation">DecFieldType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecidableFieldMixin"><span class="id" title="definition">DecidableFieldMixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.cT"><span class="id" title="variable">cT</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finComRingType"><span class="id" title="definition">finComRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComRing.Pack"><span class="id" title="constructor">ComRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finComUnitRingType"><span class="id" title="definition">finComUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.ComUnitRing.Pack"><span class="id" title="constructor">ComUnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finIdomainType"><span class="id" title="definition">finIdomainType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.IntegralDomain.Pack"><span class="id" title="constructor">IntegralDomain.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.xclass"><span class="id" title="variable">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.finZmodType"><span class="id" title="definition">finZmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.DecField.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins.cT"><span class="id" title="variable">cT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Joins"><span class="id" title="section">Joins</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.DecField.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">Field.type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.type"><span class="id" title="definition">GRing.DecidableField.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="keyword">type</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finComUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finIdomainType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.DecField"><span class="id" title="module">DecField</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Lmodule"><span class="id" title="module">Lmodule</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Lmodule.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Lmodule.ClassDef.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.Lmodule.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">M</span> :=<br/> - <a name="FinRing.Lmodule.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.Lmodule.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.class_of"><span class="id" title="record">GRing.Lmodule.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>; <a name="FinRing.Lmodule.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.Lmodule.type"><span class="id" title="record">type</span></a> (<span class="id" title="var">phR</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.R"><span class="id" title="variable">R</span></a>) := <a name="FinRing.Lmodule.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.Lmodule.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Variables</span> (<a name="FinRing.Lmodule.ClassDef.phR"><span class="id" title="variable">phR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.R"><span class="id" title="variable">R</span></a>) (<a name="FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.type"><span class="id" title="record">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.phR"><span class="id" title="variable">phR</span></a>) <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Class"><span class="id" title="constructor">Class</span></a> (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.class"><span class="id" title="definition">GRing.Lmodule.class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.Lmodule.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.lmodType"><span class="id" title="definition">lmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.Pack"><span class="id" title="constructor">GRing.Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.lmod_countType"><span class="id" title="definition">lmod_countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">lmodType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.lmod_finType"><span class="id" title="definition">lmod_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">lmodType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.lmod_baseFinGroupType"><span class="id" title="definition">lmod_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.lmod_finGroupType"><span class="id" title="definition">lmod_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmod_baseFinGroupType"><span class="id" title="definition">lmod_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.lmod_countZmodType"><span class="id" title="definition">lmod_countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lmodule.lmod_finZmodType"><span class="id" title="definition">lmod_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Import</span> <a name="FinRing.Lmodule.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base"><span class="id" title="projection">GRing.Lmodule.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.base2"><span class="id" title="definition">Zmodule.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.lmodType"><span class="id" title="definition">GRing.Lmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_countType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_countZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_finZmodType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Lmodule.Exports.finLmodType"><span class="id" title="abbreviation">finLmodType</span></a> <span class="id" title="var">R</span> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.type"><span class="id" title="record">FinRing.Lmodule.type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)).<br/> -<span class="id" title="keyword">Notation</span> <a name="89ed2b9c4fe0e2b73b78eb3dc17a4b6f"><span class="id" title="notation">"</span></a>[ 'finLmodType' R 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> (@<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">_</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)) <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finLmodType' R 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule"><span class="id" title="module">Lmodule</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Lmodule.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Lalgebra"><span class="id" title="module">Lalgebra</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Lalgebra.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.Lalgebra.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">M</span> :=<br/> - <a name="FinRing.Lalgebra.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.Lalgebra.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lalgebra.class_of"><span class="id" title="record">GRing.Lalgebra.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>; <a name="FinRing.Lalgebra.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.base2"><span class="id" title="definition">base2</span></a> <span class="id" title="var">M</span> (<span class="id" title="var">c</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>) := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Class"><span class="id" title="constructor">Ring.Class</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.mixin"><span class="id" title="projection">mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#c"><span class="id" title="variable">c</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.base3"><span class="id" title="definition">base3</span></a> <span class="id" title="var">M</span> (<span class="id" title="var">c</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>) := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Class"><span class="id" title="constructor">Lmodule.Class</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#c"><span class="id" title="variable">c</span></a>) (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.mixin"><span class="id" title="projection">mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#c"><span class="id" title="variable">c</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.Lalgebra.type"><span class="id" title="record">type</span></a> (<span class="id" title="var">phR</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a>) := <a name="FinRing.Lalgebra.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.Lalgebra.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Variables</span> (<a name="FinRing.Lalgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a>) (<a name="FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.type"><span class="id" title="record">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a>) <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Class"><span class="id" title="constructor">Class</span></a> (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lalgebra.class"><span class="id" title="definition">GRing.Lalgebra.class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.Lalgebra.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lmodType"><span class="id" title="definition">lmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.Pack"><span class="id" title="constructor">GRing.Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lalgebra.Pack"><span class="id" title="constructor">GRing.Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_countType"><span class="id" title="definition">lalg_countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_finType"><span class="id" title="definition">lalg_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_baseFinGroupType"><span class="id" title="definition">lalg_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_finGroupType"><span class="id" title="definition">lalg_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalg_baseFinGroupType"><span class="id" title="definition">lalg_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_countZmodType"><span class="id" title="definition">lalg_countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_finZmodType"><span class="id" title="definition">lalg_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_finLmodType"><span class="id" title="definition">lalg_finLmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_countRingType"><span class="id" title="definition">lalg_countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lalg_finRingType"><span class="id" title="definition">lalg_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lmod_countRingType"><span class="id" title="definition">lmod_countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.lmod_finRingType"><span class="id" title="definition">lmod_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finLmod_ringType"><span class="id" title="definition">finLmod_ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finLmod_countRingType"><span class="id" title="definition">finLmod_countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Lalgebra.finLmod_finRingType"><span class="id" title="definition">finLmod_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Lalgebra.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base"><span class="id" title="projection">GRing.Lalgebra.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base2"><span class="id" title="definition">Ring.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.base3"><span class="id" title="definition">Lmodule.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lmodType"><span class="id" title="definition">GRing.Lmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.finLmodType"><span class="id" title="definition">Lmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.lalgType"><span class="id" title="definition">GRing.Lalgebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_countType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_countZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_finLmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_countRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalg_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_countRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmod_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLmod_ringType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLmod_countRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLmod_finRingType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Lalgebra.Exports.finLalgType"><span class="id" title="abbreviation">finLalgType</span></a> <span class="id" title="var">R</span> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.type"><span class="id" title="record">FinRing.Lalgebra.type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)).<br/> -<span class="id" title="keyword">Notation</span> <a name="006f6a476eaf49ff2271764c2e9c0634"><span class="id" title="notation">"</span></a>[ 'finLalgType' R 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> (@<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">_</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)) <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finLalgType' R 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra"><span class="id" title="module">Lalgebra</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Lalgebra.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Algebra"><span class="id" title="module">Algebra</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.Algebra.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.Algebra.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">M</span> :=<br/> - <a name="FinRing.Algebra.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.Algebra.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Algebra.class_of"><span class="id" title="record">GRing.Algebra.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>; <a name="FinRing.Algebra.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.base2"><span class="id" title="definition">base2</span></a> <span class="id" title="var">M</span> (<span class="id" title="var">c</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>) := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Class"><span class="id" title="constructor">Lalgebra.Class</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.mixin"><span class="id" title="projection">mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#c"><span class="id" title="variable">c</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.Algebra.type"><span class="id" title="record">type</span></a> (<span class="id" title="var">phR</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a>) := <a name="FinRing.Algebra.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.Algebra.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Variables</span> (<a name="FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a>) (<a name="FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.type"><span class="id" title="record">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a>) <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Class"><span class="id" title="constructor">Class</span></a> (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Algebra.class"><span class="id" title="definition">GRing.Algebra.class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.Algebra.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.lmodType"><span class="id" title="definition">lmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.Pack"><span class="id" title="constructor">GRing.Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.lalgType"><span class="id" title="definition">lalgType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lalgebra.Pack"><span class="id" title="constructor">GRing.Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.finLalgType"><span class="id" title="definition">finLalgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Algebra.Pack"><span class="id" title="constructor">GRing.Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_countType"><span class="id" title="definition">alg_countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_finType"><span class="id" title="definition">alg_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_baseFinGroupType"><span class="id" title="definition">alg_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_finGroupType"><span class="id" title="definition">alg_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.alg_baseFinGroupType"><span class="id" title="definition">alg_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_countZmodType"><span class="id" title="definition">alg_countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_finZmodType"><span class="id" title="definition">alg_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_countRingType"><span class="id" title="definition">alg_countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_finRingType"><span class="id" title="definition">alg_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_finLmodType"><span class="id" title="definition">alg_finLmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Algebra.alg_finLalgType"><span class="id" title="definition">alg_finLalgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Algebra.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base"><span class="id" title="projection">GRing.Algebra.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.base2"><span class="id" title="definition">Lalgebra.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lmodType"><span class="id" title="definition">GRing.Lmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLmodType"><span class="id" title="definition">Lmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lalgType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lalgType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lalgType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.lalgType"><span class="id" title="definition">GRing.Lalgebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalgType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLalgType"><span class="id" title="definition">finLalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLalgType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLalgType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLalgType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.finLalgType"><span class="id" title="definition">Lalgebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLalgType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.algType"><span class="id" title="definition">GRing.Algebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">algType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_countType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_countZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_countRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_finLmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">alg_finLalgType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.Algebra.Exports.finAlgType"><span class="id" title="abbreviation">finAlgType</span></a> <span class="id" title="var">R</span> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.type"><span class="id" title="record">type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)).<br/> -<span class="id" title="keyword">Notation</span> <a name="e1046e375fa30252214f407945285be1"><span class="id" title="notation">"</span></a>[ 'finAlgType' R 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> (@<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">_</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)) <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finAlgType' R 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra"><span class="id" title="module">Algebra</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Algebra.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.UnitAlgebra"><span class="id" title="module">UnitAlgebra</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FinRing.UnitAlgebra.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Exports.unitRingType"><span class="id" title="abbreviation">unitRingType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Record</span> <a name="FinRing.UnitAlgebra.class_of"><span class="id" title="record">class_of</span></a> <span class="id" title="var">M</span> :=<br/> - <a name="FinRing.UnitAlgebra.Class"><span class="id" title="constructor">Class</span></a> { <a name="FinRing.UnitAlgebra.base"><span class="id" title="projection">base</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitAlgebra.class_of"><span class="id" title="record">GRing.UnitAlgebra.class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>; <a name="FinRing.UnitAlgebra.mixin"><span class="id" title="projection">mixin</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.mixin_of"><span class="id" title="abbreviation">mixin_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#base"><span class="id" title="method">base</span></a> }.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.base2"><span class="id" title="definition">base2</span></a> <span class="id" title="var">M</span> (<span class="id" title="var">c</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>) := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Class"><span class="id" title="constructor">Algebra.Class</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.mixin"><span class="id" title="projection">mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#c"><span class="id" title="variable">c</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.base3"><span class="id" title="definition">base3</span></a> <span class="id" title="var">M</span> (<span class="id" title="var">c</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#M"><span class="id" title="variable">M</span></a>) := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Class"><span class="id" title="constructor">UnitRing.Class</span></a> <span class="id" title="var">_</span> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#c"><span class="id" title="variable">c</span></a>) (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.mixin"><span class="id" title="projection">mixin</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#c"><span class="id" title="variable">c</span></a>).<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="FinRing.UnitAlgebra.type"><span class="id" title="record">type</span></a> (<span class="id" title="var">phR</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a>) := <a name="FinRing.UnitAlgebra.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="FinRing.UnitAlgebra.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#sort"><span class="id" title="method">sort</span></a>}.<br/> -<span class="id" title="keyword">Variables</span> (<a name="FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a>) (<a name="FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.type"><span class="id" title="record">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.pack"><span class="id" title="definition">pack</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.gen_pack"><span class="id" title="definition">gen_pack</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a>) <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.Class"><span class="id" title="constructor">Class</span></a> (@<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitAlgebra.class"><span class="id" title="definition">GRing.UnitAlgebra.class</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="keyword">as</span> <span class="id" title="var">cT'</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#cT'"><span class="id" title="variable">cT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/> -<span class="id" title="keyword">Let</span> <a name="FinRing.UnitAlgebra.ClassDef.xT"><span class="id" title="variable">xT</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">T</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.class"><span class="id" title="definition">class</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.class_of"><span class="id" title="record">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.xT"><span class="id" title="variable">xT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.eqType"><span class="id" title="definition">eqType</span></a> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Equality.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.choiceType"><span class="id" title="definition">choiceType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Pack"><span class="id" title="constructor">Choice.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countType"><span class="id" title="definition">countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finType"><span class="id" title="definition">finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">zmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countZmodType"><span class="id" title="definition">countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finZmodType"><span class="id" title="definition">finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.ringType"><span class="id" title="definition">ringType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countRingType"><span class="id" title="definition">countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finRingType"><span class="id" title="definition">finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">unitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Pack"><span class="id" title="constructor">GRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.UnitRing.Pack"><span class="id" title="constructor">CountRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.lmodType"><span class="id" title="definition">lmodType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.Pack"><span class="id" title="constructor">GRing.Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.lalgType"><span class="id" title="definition">lalgType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lalgebra.Pack"><span class="id" title="constructor">GRing.Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finLalgType"><span class="id" title="definition">finLalgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.algType"><span class="id" title="definition">algType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Algebra.Pack"><span class="id" title="constructor">GRing.Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finAlgType"><span class="id" title="definition">finAlgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> := @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitAlgebra.Pack"><span class="id" title="constructor">GRing.UnitAlgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finGroupType"><span class="id" title="definition">finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_countType"><span class="id" title="definition">unitAlg_countType</span></a> := @<a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Pack"><span class="id" title="constructor">Countable.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finType"><span class="id" title="definition">unitAlg_finType</span></a> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Pack"><span class="id" title="constructor">Finite.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_"><span class="id" title="abbreviation">fin_</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_baseFinGroupType"><span class="id" title="definition">unitAlg_baseFinGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.base_group"><span class="id" title="abbreviation">base_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finType"><span class="id" title="definition">finType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finGroupType"><span class="id" title="definition">unitAlg_finGroupType</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.fin_group"><span class="id" title="abbreviation">fin_group</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlg_baseFinGroupType"><span class="id" title="definition">unitAlg_baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">zmodType</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_countZmodType"><span class="id" title="definition">unitAlg_countZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Zmodule.Pack"><span class="id" title="constructor">CountRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finZmodType"><span class="id" title="definition">unitAlg_finZmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Zmodule.Pack"><span class="id" title="constructor">Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_countRingType"><span class="id" title="definition">unitAlg_countRingType</span></a> := @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.Ring.Pack"><span class="id" title="constructor">CountRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finRingType"><span class="id" title="definition">unitAlg_finRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Ring.Pack"><span class="id" title="constructor">Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_countUnitRingType"><span class="id" title="definition">unitAlg_countUnitRingType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.countalg.html#CountRing.UnitRing.Pack"><span class="id" title="constructor">CountRing.UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finUnitRingType"><span class="id" title="definition">unitAlg_finUnitRingType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitRing.Pack"><span class="id" title="constructor">UnitRing.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finLmodType"><span class="id" title="definition">unitAlg_finLmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finLalgType"><span class="id" title="definition">unitAlg_finLalgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitAlg_finAlgType"><span class="id" title="definition">unitAlg_finAlgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitRing_finLmodType"><span class="id" title="definition">unitRing_finLmodType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitRing_finLalgType"><span class="id" title="definition">unitRing_finLalgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.unitRing_finAlgType"><span class="id" title="definition">unitRing_finAlgType</span></a> := @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countUnitRing_lmodType"><span class="id" title="definition">countUnitRing_lmodType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.Pack"><span class="id" title="constructor">GRing.Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countUnitRing_finLmodType"><span class="id" title="definition">countUnitRing_finLmodType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countUnitRing_lalgType"><span class="id" title="definition">countUnitRing_lalgType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lalgebra.Pack"><span class="id" title="constructor">GRing.Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countUnitRing_finLalgType"><span class="id" title="definition">countUnitRing_finLalgType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countUnitRing_algType"><span class="id" title="definition">countUnitRing_algType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Algebra.Pack"><span class="id" title="constructor">GRing.Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.countUnitRing_finAlgType"><span class="id" title="definition">countUnitRing_finAlgType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finUnitRing_lmodType"><span class="id" title="definition">finUnitRing_lmodType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lmodule.Pack"><span class="id" title="constructor">GRing.Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finUnitRing_finLmodType"><span class="id" title="definition">finUnitRing_finLmodType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lmodule.Pack"><span class="id" title="constructor">Lmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finUnitRing_lalgType"><span class="id" title="definition">finUnitRing_lalgType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Lalgebra.Pack"><span class="id" title="constructor">GRing.Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finUnitRing_finLalgType"><span class="id" title="definition">finUnitRing_finLalgType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Lalgebra.Pack"><span class="id" title="constructor">Lalgebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finUnitRing_algType"><span class="id" title="definition">finUnitRing_algType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Algebra.Pack"><span class="id" title="constructor">GRing.Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.UnitAlgebra.finUnitRing_finAlgType"><span class="id" title="definition">finUnitRing_finAlgType</span></a> :=<br/> - @<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Algebra.Pack"><span class="id" title="constructor">Algebra.Pack</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef.phR"><span class="id" title="variable">phR</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.xclass"><span class="id" title="abbreviation">xclass</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.UnitAlgebra.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base"><span class="id" title="projection">base</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base"><span class="id" title="projection">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base"><span class="id" title="projection">GRing.UnitAlgebra.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base2"><span class="id" title="definition">base2</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base2"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base2"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base2"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base2"><span class="id" title="definition">Algebra.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base3"><span class="id" title="definition">base3</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base3"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base3"><span class="id" title="definition">class_of</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base3"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.base3"><span class="id" title="definition">UnitRing.class_of</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.sort"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.sort"><span class="id" title="projection">Sortclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.eqType"><span class="id" title="definition">eqType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.eqType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.eqType"><span class="id" title="definition">Equality.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">eqType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.choiceType"><span class="id" title="definition">choiceType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.choiceType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.choiceType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.choiceType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.choiceType"><span class="id" title="definition">Choice.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">choiceType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countType"><span class="id" title="definition">countType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countType"><span class="id" title="definition">Countable.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finType"><span class="id" title="definition">finType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finType"><span class="id" title="definition">Finite.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.baseFinGroupType"><span class="id" title="definition">baseFinGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.baseFinGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.baseFinGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.baseFinGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.baseFinGroupType"><span class="id" title="definition">FinGroup.base_type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finGroupType"><span class="id" title="definition">finGroupType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finGroupType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finGroupType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finGroupType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finGroupType"><span class="id" title="definition">FinGroup.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finGroupType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">zmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.zmodType"><span class="id" title="definition">GRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countZmodType"><span class="id" title="definition">countZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countZmodType"><span class="id" title="definition">CountRing.Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finZmodType"><span class="id" title="definition">finZmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finZmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finZmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finZmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finZmodType"><span class="id" title="definition">Zmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finZmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ringType"><span class="id" title="definition">ringType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ringType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ringType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ringType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.ringType"><span class="id" title="definition">GRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countRingType"><span class="id" title="definition">countRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countRingType"><span class="id" title="definition">CountRing.Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finRingType"><span class="id" title="definition">finRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finRingType"><span class="id" title="definition">Ring.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">unitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitRingType"><span class="id" title="definition">GRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">countUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.countUnitRingType"><span class="id" title="definition">CountRing.UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">finUnitRingType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finUnitRingType"><span class="id" title="definition">UnitRing.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRingType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lmodType"><span class="id" title="definition">lmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lmodType"><span class="id" title="definition">GRing.Lmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLmodType"><span class="id" title="definition">finLmodType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLmodType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLmodType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLmodType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLmodType"><span class="id" title="definition">Lmodule.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLmodType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lalgType"><span class="id" title="definition">lalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lalgType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lalgType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lalgType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.lalgType"><span class="id" title="definition">GRing.Lalgebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lalgType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLalgType"><span class="id" title="definition">finLalgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLalgType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLalgType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLalgType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finLalgType"><span class="id" title="definition">Lalgebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finLalgType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.algType"><span class="id" title="definition">algType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.algType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.algType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.algType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.algType"><span class="id" title="definition">GRing.Algebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">algType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finAlgType"><span class="id" title="definition">finAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finAlgType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finAlgType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finAlgType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.finAlgType"><span class="id" title="definition">Algebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finAlgType</span>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">unitAlgType</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.unitAlgType"><span class="id" title="definition">GRing.UnitAlgebra.type</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_countType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_baseFinGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finGroupType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_countZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finZmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_countRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_countUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finUnitRingType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finLmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finLalgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitAlg_finAlgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finLmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finLalgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRing_finAlgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_lmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finLmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_lalgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finLalgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_algType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">countUnitRing_finAlgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRing_lmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRing_finLmodType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRing_lalgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRing_finLalgType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRing_algType</span>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finUnitRing_finAlgType</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="FinRing.UnitAlgebra.Exports.finUnitAlgType"><span class="id" title="abbreviation">finUnitAlgType</span></a> <span class="id" title="var">R</span> := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.type"><span class="id" title="record">type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)).<br/> -<span class="id" title="keyword">Notation</span> <a name="2aaa42abe766947d0080d3fd1521c4bc"><span class="id" title="notation">"</span></a>[ 'finUnitAlgType' R 'of' T ]" := (<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.do_pack"><span class="id" title="abbreviation">do_pack</span></a> (@<a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">_</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>)) <span class="id" title="var">T</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'finUnitAlgType' R 'of' T ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.UnitAlgebra"><span class="id" title="module">UnitAlgebra</span></a>.<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">UnitAlgebra.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="FinRing.Theory"><span class="id" title="module">Theory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.zmod1gE"><span class="id" title="definition">zmod1gE</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.zmod1gE"><span class="id" title="lemma">zmod1gE</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.zmodVgE"><span class="id" title="definition">zmodVgE</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.zmodVgE"><span class="id" title="lemma">zmodVgE</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.zmodMgE"><span class="id" title="definition">zmodMgE</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.zmodMgE"><span class="id" title="lemma">zmodMgE</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.zmodXgE"><span class="id" title="definition">zmodXgE</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.zmodXgE"><span class="id" title="lemma">zmodXgE</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.zmod_mulgC"><span class="id" title="definition">zmod_mulgC</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.zmod_mulgC"><span class="id" title="lemma">zmod_mulgC</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.zmod_abelian"><span class="id" title="definition">zmod_abelian</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.zmod_abelian"><span class="id" title="lemma">zmod_abelian</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.val_unit1"><span class="id" title="definition">val_unit1</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.val_unit1"><span class="id" title="lemma">val_unit1</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.val_unitM"><span class="id" title="definition">val_unitM</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.val_unitM"><span class="id" title="lemma">val_unitM</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.val_unitX"><span class="id" title="definition">val_unitX</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.val_unitX"><span class="id" title="lemma">val_unitX</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.val_unitV"><span class="id" title="definition">val_unitV</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.val_unitV"><span class="id" title="lemma">val_unitV</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="FinRing.Theory.unit_actE"><span class="id" title="definition">unit_actE</span></a> := <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.unit_actE"><span class="id" title="lemma">unit_actE</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing.Theory"><span class="id" title="module">Theory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.finalg.html#FinRing"><span class="id" title="module">FinRing</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">FinRing</span>.<br/> -<span class="id" title="keyword">Export</span> <span class="id" title="var">Zmodule.Exports</span> <span class="id" title="var">Ring.Exports</span> <span class="id" title="var">ComRing.Exports</span>.<br/> -<span class="id" title="keyword">Export</span> <span class="id" title="var">UnitRing.Exports</span> <span class="id" title="var">UnitsGroupExports</span> <span class="id" title="var">ComUnitRing.Exports</span>.<br/> -<span class="id" title="keyword">Export</span> <span class="id" title="var">IntegralDomain.Exports</span> <span class="id" title="var">Field.Exports</span> <span class="id" title="var">DecField.Exports</span>.<br/> -<span class="id" title="keyword">Export</span> <span class="id" title="var">Lmodule.Exports</span> <span class="id" title="var">Lalgebra.Exports</span> <span class="id" title="var">Algebra.Exports</span> <span class="id" title="var">UnitAlgebra.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="18d0918a160c839bc9f32d8e64dd406d"><span class="id" title="notation">"</span></a>{ 'unit' R }" := (<a class="idref" href="mathcomp.algebra.finalg.html#unit_of"><span class="id" title="inductive">unit_of</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">R</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "{ 'unit' R }") : <span class="id" title="var">type_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="14f3b62ff45649c8c5e317a248d7a1a6"><span class="id" title="notation">"</span></a>''U'" := (<a class="idref" href="mathcomp.algebra.finalg.html#unit_action"><span class="id" title="definition">unit_action</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">action_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="28ac3fd54a63eebeca919b4aa704f80e"><span class="id" title="notation">"</span></a>''U'" := (<a class="idref" href="mathcomp.algebra.finalg.html#unit_groupAction"><span class="id" title="definition">unit_groupAction</span></a> <span class="id" title="var">_</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 8) : <span class="id" title="var">groupAction_scope</span>.<br/> -</div> -</div> - -<div id="footer"> -<hr/><a href="index.html">Index</a><hr/>This page has been generated by <a href="http://coq.inria.fr/">coqdoc</a> -</div> - -</div> - -</body> -</html>
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