diff options
| author | Enrico Tassi | 2019-05-22 13:43:08 +0200 |
|---|---|---|
| committer | Enrico Tassi | 2019-05-22 15:34:14 +0200 |
| commit | 748d716efb2f2f75946c8386e441ce1789806a39 (patch) | |
| tree | fe7bb1c5235550410c64e968f4a4d69b7f10a047 /docs/htmldoc/mathcomp.algebra.ring_quotient.html | |
| parent | 415be3b908daadabf178a292c885db78e5b2c9a4 (diff) | |
htmldoc regenerated
Diffstat (limited to 'docs/htmldoc/mathcomp.algebra.ring_quotient.html')
| -rw-r--r-- | docs/htmldoc/mathcomp.algebra.ring_quotient.html | 328 |
1 files changed, 163 insertions, 165 deletions
diff --git a/docs/htmldoc/mathcomp.algebra.ring_quotient.html b/docs/htmldoc/mathcomp.algebra.ring_quotient.html index 35d7bc6..0e42147 100644 --- a/docs/htmldoc/mathcomp.algebra.ring_quotient.html +++ b/docs/htmldoc/mathcomp.algebra.ring_quotient.html @@ -21,7 +21,6 @@ <div class="code"> <span class="comment">(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. <br/> Distributed under the terms of CeCILL-B. *)</span><br/> -<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="mathcomp.ssreflect.ssreflect.html#"><span class="id" title="library">mathcomp.ssreflect.ssreflect</span></a>.<br/> <br/> </div> @@ -67,9 +66,9 @@ unitRingQuotType ... u i == As in the previous cases, instance of unit ring whose unit predicate is obtained from u and the inverse from i. - idealr R S == (S : pred R) is a non-trivial, decidable, + idealr R S == S : {pred R} is a non-trivial, decidable, right ideal of the ring R. - prime_idealr R S == (S : pred R) is a non-trivial, decidable, + prime_idealr R S == S : {pred R} is a non-trivial, decidable, right, prime ideal of the ring R. <div class="paragraph"> </div> @@ -85,22 +84,21 @@ <div class="paragraph"> </div> - MkIdeal idealS == packs idealS : proper_ideal S into an - idealr S interface structure associating the + MkIdeal idealS == packs idealS : proper_ideal S into an idealr S + interface structure associating the idealr_closed property to the canonical pred_key S (see ssrbool), which must already - be an zmodPred (see ssralg). + be a zmodPred (see ssralg). MkPrimeIdeal pidealS == packs pidealS : prime_idealr_closed S into a prime_idealr S interface structure associating the prime_idealr_closed property to the canonical pred_key S (see ssrbool), which must already be an idealr (see above). {ideal_quot kI} == quotient by the keyed (right) ideal predicate - kI of a commutative ring R. Note that we indeed - only provide canonical structures of ring - quotients for the case of commutative rings, - for which a right ideal is obviously a - two-sided ideal. + kI of a commutative ring R. Note that we only + provide canonical structures of ring quotients + for commutative rings, in which a right ideal + is obviously a two-sided ideal. <div class="paragraph"> </div> @@ -138,18 +136,18 @@ <br/> <span class="id" title="keyword">Variable</span> (<a name="ZmodQuot.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>).<br/> -<span class="id" title="keyword">Variable</span> <a name="ZmodQuot.eqT"><span class="id" title="variable">eqT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="ZmodQuot.zeroT"><span class="id" title="variable">zeroT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>) (<a name="ZmodQuot.oppT"><span class="id" title="variable">oppT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>) (<a name="ZmodQuot.addT"><span class="id" title="variable">addT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>).<br/> +<span class="id" title="keyword">Variable</span> <a name="ZmodQuot.eqT"><span class="id" title="variable">eqT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="ZmodQuot.zeroT"><span class="id" title="variable">zeroT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>) (<a name="ZmodQuot.oppT"><span class="id" title="variable">oppT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.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.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>) (<a name="ZmodQuot.addT"><span class="id" title="variable">addT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.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.ring_quotient.html#ZmodQuot.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.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>).<br/> <br/> <span class="id" title="keyword">Record</span> <a name="zmod_quot_mixin_of"><span class="id" title="record">zmod_quot_mixin_of</span></a> (<span class="id" title="var">Q</span> : <span class="id" title="keyword">Type</span>) (<span class="id" title="var">qc</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quot_class_of"><span class="id" title="abbreviation">quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>)<br/> (<span class="id" title="var">zc</span> : <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.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>) := <a name="ZmodQuotMixinPack"><span class="id" title="constructor">ZmodQuotMixinPack</span></a> {<br/> <a name="zmod_eq_quot_mixin"><span class="id" title="projection">zmod_eq_quot_mixin</span></a> :> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#eq_quot_mixin_of"><span class="id" title="definition">eq_quot_mixin_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">/</span></a><br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.opp"><span class="id" title="definition">GRing.opp</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.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">}</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">/</span></a><br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.add"><span class="id" title="definition">GRing.add</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.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">}</span></a><br/> + <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> 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.ssralg.html#GRing.Zmodule.Pack"><span class="id" title="constructor">GRing.Zmodule.Pack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a>;<br/> + <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">:</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#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">/</span></a><br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.opp"><span class="id" title="definition">GRing.opp</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.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">}</span></a>;<br/> + <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a><br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.add"><span class="id" title="definition">GRing.add</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.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a><br/> }.<br/> <br/> @@ -164,7 +162,7 @@ <span class="id" title="keyword">Structure</span> <a name="zmodQuotType"><span class="id" title="record">zmodQuotType</span></a> : <span class="id" title="keyword">Type</span> := <a name="ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> {<br/> <a name="zmod_quot_sort"><span class="id" title="projection">zmod_quot_sort</span></a> :> <span class="id" title="keyword">Type</span>;<br/> <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class_of"><span class="id" title="record">zmod_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_sort"><span class="id" title="method">zmod_quot_sort</span></a>;<br/> - <span class="id" title="var">_</span> : <span class="id" title="keyword">Type</span><br/> + <br/> }.<br/> <br/> @@ -172,21 +170,21 @@ <br/> <span class="id" title="keyword">Definition</span> <a name="zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <span class="id" title="var">zqT</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class_of"><span class="id" title="record">zmod_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a> :=<br/> - <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">cT</span> <span class="id" title="var">_</span> <span class="id" title="keyword">as</span> <span class="id" title="var">qT'</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class_of"><span class="id" title="record">zmod_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT'"><span class="id" title="variable">qT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">cT</span>.<br/> + <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">cT</span> <span class="id" title="keyword">as</span> <span class="id" title="var">qT'</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class_of"><span class="id" title="record">zmod_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT'"><span class="id" title="variable">qT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">cT</span>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="zmod_eq_quot_class"><span class="id" title="definition">zmod_eq_quot_class</span></a> <span class="id" title="var">zqT</span> (<span class="id" title="var">zqc</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class_of"><span class="id" title="record">zmod_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>) :<br/> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#eq_quot_class_of"><span class="id" title="record">eq_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#EqQuotClass"><span class="id" title="constructor">EqQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqc"><span class="id" title="variable">zqc</span></a>.<br/> <br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodQuotType_eqType</span> <span class="id" title="var">zqT</span> := <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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodQuotType_eqType</span> <span class="id" title="var">zqT</span> := <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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodQuotType_choiceType</span> <span class="id" title="var">zqT</span> :=<br/> - <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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>.<br/> + <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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodQuotType_zmodType</span> <span class="id" title="var">zqT</span> :=<br/> - <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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodQuotType_quotType</span> <span class="id" title="var">zqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>.<br/> + <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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>).<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodQuotType_quotType</span> <span class="id" title="var">zqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">zmodQuotType_eqQuotType</span> <span class="id" title="var">zqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#EqQuotTypePack"><span class="id" title="constructor">EqQuotTypePack</span></a><br/> - (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_eq_quot_class"><span class="id" title="definition">zmod_eq_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>)) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>.<br/> + (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_eq_quot_class"><span class="id" title="definition">zmod_eq_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>)).<br/> <br/> <span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType_eqType"><span class="id" title="definition">zmodQuotType_eqType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType_eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType_eqType"><span class="id" title="definition">zmodQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType_eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType_eqType"><span class="id" title="definition">eqType</span></a>.<br/> @@ -198,32 +196,32 @@ <br/> <span class="id" title="keyword">Definition</span> <a name="ZmodQuotType_pack"><span class="id" title="definition">ZmodQuotType_pack</span></a> <span class="id" title="var">Q</span> :=<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quotType"><span class="id" title="record">quotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">zT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.zmodType"><span class="id" title="abbreviation">zmodType</span></a>) <span class="id" title="var">qc</span> <span class="id" title="var">zc</span><br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quot_class"><span class="id" title="projection">quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> & <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.class"><span class="id" title="definition">GRing.Zmodule.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zT"><span class="id" title="variable">zT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">m</span> ⇒ <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotClass"><span class="id" title="constructor">ZmodQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m"><span class="id" title="variable">m</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>.<br/> + <span class="id" title="keyword">of</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.generic_quotient.html#quot_class"><span class="id" title="projection">quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> & <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.ssralg.html#GRing.Zmodule.class"><span class="id" title="definition">GRing.Zmodule.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zT"><span class="id" title="variable">zT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> ⇒<br/> + <span class="id" title="keyword">fun</span> <span class="id" title="var">m</span> ⇒ <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotClass"><span class="id" title="constructor">ZmodQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m"><span class="id" title="variable">m</span></a>).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="ZmodQuotMixin_pack"><span class="id" title="definition">ZmodQuotMixin_pack</span></a> <span class="id" title="var">Q</span> :=<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#eqQuotType"><span class="id" title="record">eqQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.eqT"><span class="id" title="variable">eqT</span></a>) (<span class="id" title="var">qc</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#eq_quot_class_of"><span class="id" title="record">eq_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>)<br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.ssreflect.generic_quotient.html#eq_quot_class"><span class="id" title="definition">eq_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> (<span class="id" title="var">zT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.zmodType"><span class="id" title="abbreviation">zmodType</span></a>) <span class="id" title="var">zc</span> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.class"><span class="id" title="definition">GRing.Zmodule.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zT"><span class="id" title="variable">zT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> ⇒<br/> + <span class="id" title="keyword">of</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.generic_quotient.html#eq_quot_class"><span class="id" title="definition">eq_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> ⇒<br/> + <span class="id" title="keyword">fun</span> (<span class="id" title="var">zT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.zmodType"><span class="id" title="abbreviation">zmodType</span></a>) <span class="id" title="var">zc</span> <span class="id" title="keyword">of</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.ssralg.html#GRing.Zmodule.class"><span class="id" title="definition">GRing.Zmodule.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zT"><span class="id" title="variable">zT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> ⇒<br/> <span class="id" title="keyword">fun</span> <span class="id" title="var">e</span> <span class="id" title="var">m0</span> <span class="id" title="var">mN</span> <span class="id" title="var">mD</span> ⇒ @<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotMixinPack"><span class="id" title="constructor">ZmodQuotMixinPack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zc"><span class="id" title="variable">zc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m0"><span class="id" title="variable">m0</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#mN"><span class="id" title="variable">mN</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#mD"><span class="id" title="variable">mD</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="ZmodQuotType_clone"><span class="id" title="definition">ZmodQuotType_clone</span></a> (<span class="id" title="var">Q</span> : <span class="id" title="keyword">Type</span>) <span class="id" title="var">qT</span> <span class="id" title="var">cT</span><br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> := @<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>.<br/> + <span class="id" title="keyword">of</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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> := @<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="zmod_quot_mixinP"><span class="id" title="lemma">zmod_quot_mixinP</span></a> <span class="id" title="var">zqT</span> :<br/> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_mixin_of"><span class="id" title="record">zmod_quot_mixin_of</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>) (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_zeror"><span class="id" title="lemma">pi_zeror</span></a> <span class="id" title="var">zqT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_zqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 0.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_zeror"><span class="id" title="lemma">pi_zeror</span></a> <span class="id" title="var">zqT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_zqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 0.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_oppr"><span class="id" title="lemma">pi_oppr</span></a> <span class="id" title="var">zqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_zqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_oppr"><span class="id" title="lemma">pi_oppr</span></a> <span class="id" title="var">zqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_zqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">:</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#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><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.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_addr"><span class="id" title="lemma">pi_addr</span></a> <span class="id" title="var">zqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_zqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#ae4d81913e6239182a9ac7467ffde8cd"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_addr"><span class="id" title="lemma">pi_addr</span></a> <span class="id" title="var">zqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_zqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_zero_quot_morph</span> <span class="id" title="var">zqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiMorph"><span class="id" title="abbreviation">PiMorph</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#pi_zeror"><span class="id" title="lemma">pi_zeror</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zqT"><span class="id" title="variable">zqT</span></a>).<br/> @@ -235,22 +233,22 @@ <br/> <span class="id" title="keyword">Notation</span> <a name="ZmodQuotType"><span class="id" title="abbreviation">ZmodQuotType</span></a> <span class="id" title="var">z</span> <span class="id" title="var">o</span> <span class="id" title="var">a</span> <span class="id" title="var">Q</span> <span class="id" title="var">m</span> :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotType_pack"><span class="id" title="definition">ZmodQuotType_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">z</span> <span class="id" title="var">o</span> <span class="id" title="var">a</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">m</span>).<br/> -<span class="id" title="keyword">Notation</span> <a name="b68f73bafc39ba549c2b0787edb63b18"><span class="id" title="notation">"</span></a>[ 'zmodQuotType' z , o & a 'of' Q ]" :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotType_clone"><span class="id" title="definition">ZmodQuotType_clone</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">z</span> <span class="id" title="var">o</span> <span class="id" title="var">a</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotType_pack"><span class="id" title="definition">ZmodQuotType_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">z</span> <span class="id" title="var">o</span> <span class="id" title="var">a</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <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> <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">m</span>).<br/> +<span class="id" title="keyword">Notation</span> <a name="9d7c8a06c13caaefcce95bfb77aaf6b5"><span class="id" title="notation">"</span></a>[ 'zmodQuotType' z , o & a 'of' Q ]" :=<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotType_clone"><span class="id" title="definition">ZmodQuotType_clone</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">z</span> <span class="id" title="var">o</span> <span class="id" title="var">a</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <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> "[ 'zmodQuotType' z , o & a 'of' Q ]") : <span class="id" title="var">form_scope</span>.<br/> <span class="id" title="keyword">Notation</span> <a name="ZmodQuotMixin"><span class="id" title="abbreviation">ZmodQuotMixin</span></a> <span class="id" title="var">Q</span> <span class="id" title="var">m0</span> <span class="id" title="var">mN</span> <span class="id" title="var">mD</span> :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotMixin_pack"><span class="id" title="definition">ZmodQuotMixin_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> (<a class="idref" href="mathcomp.ssreflect.generic_quotient.html#pi_eq_quot"><span class="id" title="lemma">pi_eq_quot</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">m0</span> <span class="id" title="var">mN</span> <span class="id" title="var">mD</span>).<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotMixin_pack"><span class="id" title="definition">ZmodQuotMixin_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <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> <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> (<a class="idref" href="mathcomp.ssreflect.generic_quotient.html#pi_eq_quot"><span class="id" title="lemma">pi_eq_quot</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">m0</span> <span class="id" title="var">mN</span> <span class="id" title="var">mD</span>).<br/> <br/> <span class="id" title="keyword">Section</span> <a name="PiAdditive"><span class="id" title="section">PiAdditive</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="PiAdditive.V"><span class="id" title="variable">V</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.zmodType"><span class="id" title="abbreviation">zmodType</span></a>) (<a name="PiAdditive.equivV"><span class="id" title="variable">equivV</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#V"><span class="id" title="variable">V</span></a>) (<a name="PiAdditive.zeroV"><span class="id" title="variable">zeroV</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#V"><span class="id" title="variable">V</span></a>).<br/> -<span class="id" title="keyword">Variable</span> <a name="PiAdditive.Q"><span class="id" title="variable">Q</span></a> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType"><span class="id" title="record">zmodQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiAdditive.V"><span class="id" title="variable">V</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiAdditive.equivV"><span class="id" title="variable">equivV</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiAdditive.zeroV"><span class="id" title="variable">zeroV</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">R</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="PiAdditive.V"><span class="id" title="variable">V</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.zmodType"><span class="id" title="abbreviation">zmodType</span></a>) (<a name="PiAdditive.equivV"><span class="id" title="variable">equivV</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#V"><span class="id" title="variable">V</span></a>) (<a name="PiAdditive.zeroV"><span class="id" title="variable">zeroV</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#V"><span class="id" title="variable">V</span></a>).<br/> +<span class="id" title="keyword">Variable</span> <a name="PiAdditive.Q"><span class="id" title="variable">Q</span></a> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType"><span class="id" title="record">zmodQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiAdditive.V"><span class="id" title="variable">V</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiAdditive.equivV"><span class="id" title="variable">equivV</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiAdditive.zeroV"><span class="id" title="variable">zeroV</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">R</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_is_additive"><span class="id" title="lemma">pi_is_additive</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Additive.Exports.additive"><span class="id" title="abbreviation">additive</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_Q</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_is_additive"><span class="id" title="lemma">pi_is_additive</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Additive.Exports.additive"><span class="id" title="abbreviation">additive</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_Q</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_additive</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Additive.Exports.Additive"><span class="id" title="abbreviation">Additive</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#pi_is_additive"><span class="id" title="lemma">pi_is_additive</span></a>.<br/> @@ -263,17 +261,17 @@ <br/> <span class="id" title="keyword">Variable</span> (<a name="RingQuot.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>).<br/> -<span class="id" title="keyword">Variable</span> <a name="RingQuot.eqT"><span class="id" title="variable">eqT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="RingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="RingQuot.oppT"><span class="id" title="variable">oppT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="RingQuot.addT"><span class="id" title="variable">addT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="RingQuot.oneT"><span class="id" title="variable">oneT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="RingQuot.mulT"><span class="id" title="variable">mulT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>).<br/> +<span class="id" title="keyword">Variable</span> <a name="RingQuot.eqT"><span class="id" title="variable">eqT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="RingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="RingQuot.oppT"><span class="id" title="variable">oppT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.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.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="RingQuot.addT"><span class="id" title="variable">addT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.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.ring_quotient.html#RingQuot.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.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="RingQuot.oneT"><span class="id" title="variable">oneT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="RingQuot.mulT"><span class="id" title="variable">mulT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.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.ring_quotient.html#RingQuot.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.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>).<br/> <br/> <span class="id" title="keyword">Record</span> <a name="ring_quot_mixin_of"><span class="id" title="record">ring_quot_mixin_of</span></a> (<span class="id" title="var">Q</span> : <span class="id" title="keyword">Type</span>) (<span class="id" title="var">qc</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quot_class_of"><span class="id" title="abbreviation">quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>)<br/> (<span class="id" title="var">rc</span> : <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.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>) := <a name="RingQuotMixinPack"><span class="id" title="constructor">RingQuotMixinPack</span></a> {<br/> <a name="ring_zmod_quot_mixin"><span class="id" title="projection">ring_zmod_quot_mixin</span></a> :> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_mixin_of"><span class="id" title="record">zmod_quot_mixin_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.oneT"><span class="id" title="variable">oneT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:></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.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">/</span></a><br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.mulT"><span class="id" title="variable">mulT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.mul"><span class="id" title="definition">GRing.mul</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.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">}</span></a><br/> + <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.oneT"><span class="id" title="variable">oneT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Pack"><span class="id" title="constructor">GRing.Ring.Pack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a>;<br/> + <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a><br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.mulT"><span class="id" title="variable">mulT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.mul"><span class="id" title="definition">GRing.mul</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.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a><br/> }.<br/> <br/> @@ -288,7 +286,7 @@ <span class="id" title="keyword">Structure</span> <a name="ringQuotType"><span class="id" title="record">ringQuotType</span></a> : <span class="id" title="keyword">Type</span> := <a name="RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> {<br/> <a name="ring_quot_sort"><span class="id" title="projection">ring_quot_sort</span></a> :> <span class="id" title="keyword">Type</span>;<br/> <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class_of"><span class="id" title="record">ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_sort"><span class="id" title="method">ring_quot_sort</span></a>;<br/> - <span class="id" title="var">_</span> : <span class="id" title="keyword">Type</span><br/> + <br/> }.<br/> <br/> @@ -296,7 +294,7 @@ <br/> <span class="id" title="keyword">Definition</span> <a name="ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class_of"><span class="id" title="record">ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a> :=<br/> - <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">cT</span> <span class="id" title="var">_</span> <span class="id" title="keyword">as</span> <span class="id" title="var">qT'</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class_of"><span class="id" title="record">ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT'"><span class="id" title="variable">qT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">cT</span>.<br/> + <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">cT</span> <span class="id" title="keyword">as</span> <span class="id" title="var">qT'</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class_of"><span class="id" title="record">ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT'"><span class="id" title="variable">qT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">cT</span>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="ring_zmod_quot_class"><span class="id" title="definition">ring_zmod_quot_class</span></a> <span class="id" title="var">rqT</span> (<span class="id" title="var">rqc</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class_of"><span class="id" title="record">ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) :<br/> @@ -305,17 +303,17 @@ <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#eq_quot_class_of"><span class="id" title="record">eq_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#EqQuotClass"><span class="id" title="constructor">EqQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqc"><span class="id" title="variable">rqc</span></a>.<br/> <br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_eqType</span> <span class="id" title="var">rqT</span> := <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_choiceType</span> <span class="id" title="var">rqT</span> := <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_eqType</span> <span class="id" title="var">rqT</span> := <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_choiceType</span> <span class="id" title="var">rqT</span> := <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_zmodType</span> <span class="id" title="var">rqT</span> :=<br/> - <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_ringType</span> <span class="id" title="var">rqT</span> :=<br/> - <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_quotType</span> <span class="id" title="var">rqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_quotType</span> <span class="id" title="var">rqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_eqQuotType</span> <span class="id" title="var">rqT</span> :=<br/> - <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#EqQuotTypePack"><span class="id" title="constructor">EqQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_eq_quot_class"><span class="id" title="definition">ring_eq_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#EqQuotTypePack"><span class="id" title="constructor">EqQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_eq_quot_class"><span class="id" title="definition">ring_eq_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">ringQuotType_zmodQuotType</span> <span class="id" title="var">rqT</span> :=<br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_zmod_quot_class"><span class="id" title="definition">ring_zmod_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_zmod_quot_class"><span class="id" title="definition">ring_zmod_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)).<br/> <br/> <span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType_eqType"><span class="id" title="definition">ringQuotType_eqType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType_eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType_eqType"><span class="id" title="definition">ringQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType_eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType_eqType"><span class="id" title="definition">eqType</span></a>.<br/> @@ -329,30 +327,30 @@ <br/> <span class="id" title="keyword">Definition</span> <a name="RingQuotType_pack"><span class="id" title="definition">RingQuotType_pack</span></a> <span class="id" title="var">Q</span> :=<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quotType"><span class="id" title="record">quotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">zT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) <span class="id" title="var">qc</span> <span class="id" title="var">rc</span><br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quot_class"><span class="id" title="projection">quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> & <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.class"><span class="id" title="definition">GRing.Ring.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zT"><span class="id" title="variable">zT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">m</span> ⇒ <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotClass"><span class="id" title="constructor">RingQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m"><span class="id" title="variable">m</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>.<br/> + <span class="id" title="keyword">of</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.generic_quotient.html#quot_class"><span class="id" title="projection">quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> & <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.ssralg.html#GRing.Ring.class"><span class="id" title="definition">GRing.Ring.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zT"><span class="id" title="variable">zT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> + <span class="id" title="keyword">fun</span> <span class="id" title="var">m</span> ⇒ <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotClass"><span class="id" title="constructor">RingQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m"><span class="id" title="variable">m</span></a>).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="RingQuotMixin_pack"><span class="id" title="definition">RingQuotMixin_pack</span></a> <span class="id" title="var">Q</span> :=<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qT</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodQuotType"><span class="id" title="record">zmodQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.addT"><span class="id" title="variable">addT</span></a>) ⇒<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qc</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class_of"><span class="id" title="record">zmod_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>)<br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> (<span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) <span class="id" title="var">rc</span> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.class"><span class="id" title="definition">GRing.Ring.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rT"><span class="id" title="variable">rT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> + <span class="id" title="keyword">of</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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> ⇒<br/> + <span class="id" title="keyword">fun</span> (<span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) <span class="id" title="var">rc</span> <span class="id" title="keyword">of</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.ssralg.html#GRing.Ring.class"><span class="id" title="definition">GRing.Ring.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rT"><span class="id" title="variable">rT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> <span class="id" title="keyword">fun</span> <span class="id" title="var">mZ</span> <span class="id" title="var">m1</span> <span class="id" title="var">mM</span> ⇒ @<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotMixinPack"><span class="id" title="constructor">RingQuotMixinPack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#mZ"><span class="id" title="variable">mZ</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#mM"><span class="id" title="variable">mM</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="RingQuotType_clone"><span class="id" title="definition">RingQuotType_clone</span></a> (<span class="id" title="var">Q</span> : <span class="id" title="keyword">Type</span>) <span class="id" title="var">qT</span> <span class="id" title="var">cT</span><br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> := @<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>.<br/> + <span class="id" title="keyword">of</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.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> := @<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="ring_quot_mixinP"><span class="id" title="lemma">ring_quot_mixinP</span></a> <span class="id" title="var">rqT</span> :<br/> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_mixin_of"><span class="id" title="record">ring_quot_mixin_of</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) (<a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class"><span class="id" title="definition">ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_oner"><span class="id" title="lemma">pi_oner</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.oneT"><span class="id" title="variable">oneT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 1.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_oner"><span class="id" title="lemma">pi_oner</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.oneT"><span class="id" title="variable">oneT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_mulr"><span class="id" title="lemma">pi_mulr</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.mulT"><span class="id" title="variable">mulT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_mulr"><span class="id" title="lemma">pi_mulr</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuot.mulT"><span class="id" title="variable">mulT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_one_quot_morph</span> <span class="id" title="var">rqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiMorph"><span class="id" title="abbreviation">PiMorph</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#pi_oner"><span class="id" title="lemma">pi_oner</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> @@ -363,24 +361,24 @@ <br/> <span class="id" title="keyword">Notation</span> <a name="RingQuotType"><span class="id" title="abbreviation">RingQuotType</span></a> <span class="id" title="var">o</span> <span class="id" title="var">mul</span> <span class="id" title="var">Q</span> <span class="id" title="var">mix</span> :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotType_pack"><span class="id" title="definition">RingQuotType_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">o</span> <span class="id" title="var">mul</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">mix</span>).<br/> -<span class="id" title="keyword">Notation</span> <a name="f8690bec8fb96ac4882c6825e7ed98ae"><span class="id" title="notation">"</span></a>[ 'ringQuotType' o & m 'of' Q ]" :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotType_clone"><span class="id" title="definition">RingQuotType_clone</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">o</span> <span class="id" title="var">m</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotType_pack"><span class="id" title="definition">RingQuotType_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">o</span> <span class="id" title="var">mul</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <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> <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">mix</span>).<br/> +<span class="id" title="keyword">Notation</span> <a name="6467cc36e93b35bfeb9b8e089044bdb9"><span class="id" title="notation">"</span></a>[ 'ringQuotType' o & m 'of' Q ]" :=<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotType_clone"><span class="id" title="definition">RingQuotType_clone</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">o</span> <span class="id" title="var">m</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <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> "[ 'ringQuotType' o & m 'of' Q ]") : <span class="id" title="var">form_scope</span>.<br/> <span class="id" title="keyword">Notation</span> <a name="RingQuotMixin"><span class="id" title="abbreviation">RingQuotMixin</span></a> <span class="id" title="var">Q</span> <span class="id" title="var">m1</span> <span class="id" title="var">mM</span> :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotMixin_pack"><span class="id" title="definition">RingQuotMixin_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_mixinP"><span class="id" title="lemma">zmod_quot_mixinP</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">m1</span> <span class="id" title="var">mM</span>).<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotMixin_pack"><span class="id" title="definition">RingQuotMixin_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <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> <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> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_mixinP"><span class="id" title="lemma">zmod_quot_mixinP</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">m1</span> <span class="id" title="var">mM</span>).<br/> <br/> <span class="id" title="keyword">Section</span> <a name="PiRMorphism"><span class="id" title="section">PiRMorphism</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="PiRMorphism.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>) (<a name="PiRMorphism.equivR"><span class="id" title="variable">equivR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) (<a name="PiRMorphism.zeroR"><span class="id" title="variable">zeroR</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="PiRMorphism.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>) (<a name="PiRMorphism.equivR"><span class="id" title="variable">equivR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) (<a name="PiRMorphism.zeroR"><span class="id" title="variable">zeroR</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>).<br/> <br/> -<span class="id" title="keyword">Variable</span> <a name="PiRMorphism.Q"><span class="id" title="variable">Q</span></a> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType"><span class="id" title="record">ringQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiRMorphism.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiRMorphism.equivR"><span class="id" title="variable">equivR</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiRMorphism.zeroR"><span class="id" title="variable">zeroR</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">R</span></a> 1 <a class="idref" href="mathcomp.algebra.ssralg.html#d5d4e2467843f67554f1a8a22d125de9"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#d5d4e2467843f67554f1a8a22d125de9"><span class="id" title="notation">R</span></a>.<br/> +<span class="id" title="keyword">Variable</span> <a name="PiRMorphism.Q"><span class="id" title="variable">Q</span></a> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType"><span class="id" title="record">ringQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiRMorphism.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiRMorphism.equivR"><span class="id" title="variable">equivR</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#PiRMorphism.zeroR"><span class="id" title="variable">zeroR</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">R</span></a> 1 <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>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_is_multiplicative"><span class="id" title="lemma">pi_is_multiplicative</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.RMorphism.Exports.multiplicative"><span class="id" title="abbreviation">multiplicative</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_Q</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_is_multiplicative"><span class="id" title="lemma">pi_is_multiplicative</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.RMorphism.Exports.multiplicative"><span class="id" title="abbreviation">multiplicative</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_Q</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_rmorphism</span> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.RMorphism.Exports.AddRMorphism"><span class="id" title="abbreviation">AddRMorphism</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#pi_is_multiplicative"><span class="id" title="lemma">pi_is_multiplicative</span></a>.<br/> @@ -393,20 +391,20 @@ <br/> <span class="id" title="keyword">Variable</span> (<a name="UnitRingQuot.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>).<br/> -<span class="id" title="keyword">Variable</span> <a name="UnitRingQuot.eqT"><span class="id" title="variable">eqT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="UnitRingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.oppT"><span class="id" title="variable">oppT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.addT"><span class="id" title="variable">addT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="UnitRingQuot.oneT"><span class="id" title="variable">oneT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.mulT"><span class="id" title="variable">mulT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="UnitRingQuot.unitT"><span class="id" title="variable">unitT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.invT"><span class="id" title="variable">invT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>).<br/> +<span class="id" title="keyword">Variable</span> <a name="UnitRingQuot.eqT"><span class="id" title="variable">eqT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>.<br/> +<span class="id" title="keyword">Variables</span> (<a name="UnitRingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.oppT"><span class="id" title="variable">oppT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.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.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.addT"><span class="id" title="variable">addT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.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.ring_quotient.html#UnitRingQuot.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.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="UnitRingQuot.oneT"><span class="id" title="variable">oneT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.mulT"><span class="id" title="variable">mulT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.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.ring_quotient.html#UnitRingQuot.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.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="UnitRingQuot.unitT"><span class="id" title="variable">unitT</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<a name="UnitRingQuot.invT"><span class="id" title="variable">invT</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.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.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>).<br/> <br/> <span class="id" title="keyword">Record</span> <a name="unit_ring_quot_mixin_of"><span class="id" title="record">unit_ring_quot_mixin_of</span></a> (<span class="id" title="var">Q</span> : <span class="id" title="keyword">Type</span>) (<span class="id" title="var">qc</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quot_class_of"><span class="id" title="abbreviation">quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>)<br/> (<span class="id" title="var">rc</span> : <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.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>) := <a name="UnitRingQuotMixinPack"><span class="id" title="constructor">UnitRingQuotMixinPack</span></a> {<br/> <a name="unit_ring_zmod_quot_mixin"><span class="id" title="projection">unit_ring_zmod_quot_mixin</span></a> :><br/> <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_mixin_of"><span class="id" title="record">ring_quot_mixin_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.oneT"><span class="id" title="variable">oneT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.mulT"><span class="id" title="variable">mulT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">/</span></a><br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.unitT"><span class="id" title="variable">unitT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</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.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">}</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">/</span></a><br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.invT"><span class="id" title="variable">invT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.inv"><span class="id" title="definition">GRing.inv</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.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">}</span></a><br/> + <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">:</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#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">/</span></a><br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.unitT"><span class="id" title="variable">unitT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</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.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">}</span></a>;<br/> + <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">:</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#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">/</span></a><br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.invT"><span class="id" title="variable">invT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">>-></span></a> @<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.inv"><span class="id" title="definition">GRing.inv</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.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">}</span></a><br/> }.<br/> <br/> @@ -421,7 +419,7 @@ <span class="id" title="keyword">Structure</span> <a name="unitRingQuotType"><span class="id" title="record">unitRingQuotType</span></a> : <span class="id" title="keyword">Type</span> := <a name="UnitRingQuotTypePack"><span class="id" title="constructor">UnitRingQuotTypePack</span></a> {<br/> <a name="unit_ring_quot_sort"><span class="id" title="projection">unit_ring_quot_sort</span></a> :> <span class="id" title="keyword">Type</span>;<br/> <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class_of"><span class="id" title="record">unit_ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_sort"><span class="id" title="method">unit_ring_quot_sort</span></a>;<br/> - <span class="id" title="var">_</span> : <span class="id" title="keyword">Type</span><br/> + <br/> }.<br/> <br/> @@ -429,7 +427,7 @@ <br/> <span class="id" title="keyword">Definition</span> <a name="unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class_of"><span class="id" title="record">unit_ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a> :=<br/> - <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotTypePack"><span class="id" title="constructor">UnitRingQuotTypePack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">cT</span> <span class="id" title="var">_</span> <span class="id" title="keyword">as</span> <span class="id" title="var">qT'</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a><br/> + <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotTypePack"><span class="id" title="constructor">UnitRingQuotTypePack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">cT</span> <span class="id" title="keyword">as</span> <span class="id" title="var">qT'</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a><br/> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class_of"><span class="id" title="record">unit_ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT'"><span class="id" title="variable">qT'</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">cT</span>.<br/> <br/> @@ -442,23 +440,23 @@ <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_eqType</span> <span class="id" title="var">rqT</span> :=<br/> - <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_choiceType</span> <span class="id" title="var">rqT</span> :=<br/> - <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_zmodType</span> <span class="id" title="var">rqT</span> :=<br/> - <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_ringType</span> <span class="id" title="var">rqT</span> :=<br/> - <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_unitRingType</span> <span class="id" title="var">rqT</span> :=<br/> - <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_quotType</span> <span class="id" title="var">rqT</span> :=<br/> - <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#QuotTypePack"><span class="id" title="constructor">QuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_eqQuotType</span> <span class="id" title="var">rqT</span> :=<br/> - <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#EqQuotTypePack"><span class="id" title="constructor">EqQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_eq_quot_class"><span class="id" title="definition">unit_ring_eq_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#EqQuotTypePack"><span class="id" title="constructor">EqQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_eq_quot_class"><span class="id" title="definition">unit_ring_eq_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_zmodQuotType</span> <span class="id" title="var">rqT</span> :=<br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_zmod_quot_class"><span class="id" title="definition">unit_ring_zmod_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotTypePack"><span class="id" title="constructor">ZmodQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_zmod_quot_class"><span class="id" title="definition">unit_ring_zmod_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)).<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">unitRingQuotType_ringQuotType</span> <span class="id" title="var">rqT</span> :=<br/> - <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_ring_quot_class"><span class="id" title="definition">unit_ring_ring_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>.<br/> + <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotTypePack"><span class="id" title="constructor">RingQuotTypePack</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_ring_quot_class"><span class="id" title="definition">unit_ring_ring_quot_class</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>)).<br/> <br/> <span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unitRingQuotType_eqType"><span class="id" title="definition">unitRingQuotType_eqType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unitRingQuotType_eqType"><span class="id" title="definition">:</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unitRingQuotType_eqType"><span class="id" title="definition">unitRingQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unitRingQuotType_eqType"><span class="id" title="definition">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unitRingQuotType_eqType"><span class="id" title="definition">eqType</span></a>.<br/> @@ -474,30 +472,30 @@ <br/> <span class="id" title="keyword">Definition</span> <a name="UnitRingQuotType_pack"><span class="id" title="definition">UnitRingQuotType_pack</span></a> <span class="id" title="var">Q</span> :=<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qT</span> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quotType"><span class="id" title="record">quotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Exports.unitRingType"><span class="id" title="abbreviation">unitRingType</span></a>) <span class="id" title="var">qc</span> <span class="id" title="var">rc</span><br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.ssreflect.generic_quotient.html#quot_class"><span class="id" title="projection">quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> & <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.class"><span class="id" title="definition">GRing.UnitRing.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rT"><span class="id" title="variable">rT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">m</span> ⇒ <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotTypePack"><span class="id" title="constructor">UnitRingQuotTypePack</span></a> (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotClass"><span class="id" title="constructor">UnitRingQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m"><span class="id" title="variable">m</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>.<br/> + <span class="id" title="keyword">of</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.generic_quotient.html#quot_class"><span class="id" title="projection">quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> & <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.ssralg.html#GRing.UnitRing.class"><span class="id" title="definition">GRing.UnitRing.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rT"><span class="id" title="variable">rT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> + <span class="id" title="keyword">fun</span> <span class="id" title="var">m</span> ⇒ <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotTypePack"><span class="id" title="constructor">UnitRingQuotTypePack</span></a> (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotClass"><span class="id" title="constructor">UnitRingQuotClass</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#m"><span class="id" title="variable">m</span></a>).<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="UnitRingQuotMixin_pack"><span class="id" title="definition">UnitRingQuotMixin_pack</span></a> <span class="id" title="var">Q</span> :=<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qT</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ringQuotType"><span class="id" title="record">ringQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.oneT"><span class="id" title="variable">oneT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.mulT"><span class="id" title="variable">mulT</span></a>) ⇒<br/> <span class="id" title="keyword">fun</span> (<span class="id" title="var">qc</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#ring_quot_class_of"><span class="id" title="record">ring_quot_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.eqT"><span class="id" title="variable">eqT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.zeroT"><span class="id" title="variable">zeroT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.oppT"><span class="id" title="variable">oppT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.addT"><span class="id" title="variable">addT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.oneT"><span class="id" title="variable">oneT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.mulT"><span class="id" title="variable">mulT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>)<br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> (<span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Exports.unitRingType"><span class="id" title="abbreviation">unitRingType</span></a>) <span class="id" title="var">rc</span> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.class"><span class="id" title="definition">GRing.UnitRing.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rT"><span class="id" title="variable">rT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> + <span class="id" title="keyword">of</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.ring_quotient.html#zmod_quot_class"><span class="id" title="definition">zmod_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> ⇒<br/> + <span class="id" title="keyword">fun</span> (<span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.UnitRing.Exports.unitRingType"><span class="id" title="abbreviation">unitRingType</span></a>) <span class="id" title="var">rc</span> <span class="id" title="keyword">of</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.ssralg.html#GRing.UnitRing.class"><span class="id" title="definition">GRing.UnitRing.class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rT"><span class="id" title="variable">rT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> ⇒<br/> <span class="id" title="keyword">fun</span> <span class="id" title="var">mR</span> <span class="id" title="var">mU</span> <span class="id" title="var">mV</span> ⇒ @<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotMixinPack"><span class="id" title="constructor">UnitRingQuotMixinPack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qc"><span class="id" title="variable">qc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rc"><span class="id" title="variable">rc</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#mR"><span class="id" title="variable">mR</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#mU"><span class="id" title="variable">mU</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#mV"><span class="id" title="variable">mV</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="UnitRingQuotType_clone"><span class="id" title="definition">UnitRingQuotType_clone</span></a> (<span class="id" title="var">Q</span> : <span class="id" title="keyword">Type</span>) <span class="id" title="var">qT</span> <span class="id" title="var">cT</span><br/> - <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> := @<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotTypePack"><span class="id" title="constructor">UnitRingQuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a>.<br/> + <span class="id" title="keyword">of</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.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#qT"><span class="id" title="variable">qT</span></a>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a> := @<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotTypePack"><span class="id" title="constructor">UnitRingQuotTypePack</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#cT"><span class="id" title="variable">cT</span></a>.<br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="unit_ring_quot_mixinP"><span class="id" title="lemma">unit_ring_quot_mixinP</span></a> <span class="id" title="var">rqT</span> :<br/> <a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_mixin_of"><span class="id" title="record">unit_ring_quot_mixin_of</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>) (<a class="idref" href="mathcomp.algebra.ring_quotient.html#unit_ring_quot_class"><span class="id" title="definition">unit_ring_quot_class</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_unitr"><span class="id" title="lemma">pi_unitr</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.unitT"><span class="id" title="variable">unitT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#fcecf6c7c5b99f975a4e95451ce580e5"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_unitr"><span class="id" title="lemma">pi_unitr</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">:</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#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.unitT"><span class="id" title="variable">unitT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.unit"><span class="id" title="definition">GRing.unit</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#96bead841b87c72f1ae1be942b541e72"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="pi_invr"><span class="id" title="lemma">pi_invr</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#997e4486c98ae8c7d206ef25b33fb606"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.invT"><span class="id" title="variable">invT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#f3016d4e55aa553d3e912592ec65e342"><span class="id" title="notation">^-1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="pi_invr"><span class="id" title="lemma">pi_invr</span></a> <span class="id" title="var">rqT</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#3337bf2cd4a8dc684c396fc9814b46a9"><span class="id" title="notation">pi_rqT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">:</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#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuot.invT"><span class="id" title="variable">invT</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_unit_quot_morph</span> <span class="id" title="var">rqT</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiMono1"><span class="id" title="abbreviation">PiMono1</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#pi_unitr"><span class="id" title="lemma">pi_unitr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#rqT"><span class="id" title="variable">rqT</span></a>).<br/> @@ -508,68 +506,68 @@ <br/> <span class="id" title="keyword">Notation</span> <a name="UnitRingQuotType"><span class="id" title="abbreviation">UnitRingQuotType</span></a> <span class="id" title="var">u</span> <span class="id" title="var">i</span> <span class="id" title="var">Q</span> <span class="id" title="var">mix</span> :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotType_pack"><span class="id" title="definition">UnitRingQuotType_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">u</span> <span class="id" title="var">i</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">mix</span>).<br/> -<span class="id" title="keyword">Notation</span> <a name="1b5f59afaa9b0fca65e0abdceed3449f"><span class="id" title="notation">"</span></a>[ 'unitRingQuotType' u & i 'of' Q ]" :=<br/> - (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotType_clone"><span class="id" title="definition">UnitRingQuotType_clone</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">u</span> <span class="id" title="var">i</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotType_pack"><span class="id" title="definition">UnitRingQuotType_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">u</span> <span class="id" title="var">i</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <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> <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">mix</span>).<br/> +<span class="id" title="keyword">Notation</span> <a name="3dfada17667595a9eaae80400a68c9c7"><span class="id" title="notation">"</span></a>[ 'unitRingQuotType' u & i 'of' Q ]" :=<br/> + (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotType_clone"><span class="id" title="definition">UnitRingQuotType_clone</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">u</span> <span class="id" title="var">i</span> <span class="id" title="var">Q</span> <span class="id" title="var">_</span> <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> "[ 'unitRingQuotType' u & i 'of' Q ]") : <span class="id" title="var">form_scope</span>.<br/> <span class="id" title="keyword">Notation</span> <a name="UnitRingQuotMixin"><span class="id" title="abbreviation">UnitRingQuotMixin</span></a> <span class="id" title="var">Q</span> <span class="id" title="var">mU</span> <span class="id" title="var">mV</span> :=<br/> (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#UnitRingQuotMixin_pack"><span class="id" title="definition">UnitRingQuotMixin_pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">Q</span><br/> - <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_mixinP"><span class="id" title="lemma">zmod_quot_mixinP</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">mU</span> <span class="id" title="var">mV</span>).<br/> + <span class="id" title="var">_</span> <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> <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> (<a class="idref" href="mathcomp.algebra.ring_quotient.html#zmod_quot_mixinP"><span class="id" title="lemma">zmod_quot_mixinP</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">mU</span> <span class="id" title="var">mV</span>).<br/> <br/> <span class="id" title="keyword">Section</span> <a name="IdealDef"><span class="id" title="section">IdealDef</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="proper_ideal"><span class="id" title="definition">proper_ideal</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/> - 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span>, <a class="idref" href="mathcomp.algebra.ring_quotient.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="proper_ideal"><span class="id" title="definition">proper_ideal</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/> + 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#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.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span>, <a class="idref" href="mathcomp.algebra.ring_quotient.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="prime_idealr_closed"><span class="id" title="definition">prime_idealr_closed</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/> - <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span>, <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="prime_idealr_closed"><span class="id" title="definition">prime_idealr_closed</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/> + <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span>, <a class="idref" href="mathcomp.algebra.ring_quotient.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.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="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.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="idealr_closed"><span class="id" title="definition">idealr_closed</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) :=<br/> - <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">[/\</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">,</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">&</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span>, <a class="idref" href="mathcomp.algebra.ring_quotient.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#ae4d81913e6239182a9ac7467ffde8cd"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#962a3cb7af009aedac7986e261646bd1"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="idealr_closed"><span class="id" title="definition">idealr_closed</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :=<br/> + <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span>, <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span>, <a class="idref" href="mathcomp.algebra.ring_quotient.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="idealr_closed_nontrivial"><span class="id" title="lemma">idealr_closed_nontrivial</span></a> <span class="id" title="var">R</span> <span class="id" title="var">S</span> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed"><span class="id" title="definition">idealr_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#proper_ideal"><span class="id" title="definition">proper_ideal</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="idealr_closed_nontrivial"><span class="id" title="lemma">idealr_closed_nontrivial</span></a> <span class="id" title="var">R</span> <span class="id" title="var">S</span> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed"><span class="id" title="definition">idealr_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#proper_ideal"><span class="id" title="definition">proper_ideal</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="idealr_closedB"><span class="id" title="lemma">idealr_closedB</span></a> <span class="id" title="var">R</span> <span class="id" title="var">S</span> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed"><span class="id" title="definition">idealr_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmod_closed"><span class="id" title="abbreviation">zmod_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="idealr_closedB"><span class="id" title="lemma">idealr_closedB</span></a> <span class="id" title="var">R</span> <span class="id" title="var">S</span> : @<a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed"><span class="id" title="definition">idealr_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmod_closed"><span class="id" title="abbreviation">zmod_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a>.<br/> <br/> <span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closedB"><span class="id" title="lemma">idealr_closedB</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closedB"><span class="id" title="lemma">:</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closedB"><span class="id" title="lemma">idealr_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closedB"><span class="id" title="lemma">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closedB"><span class="id" title="lemma">zmod_closed</span></a>.<br/> <span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed_nontrivial"><span class="id" title="lemma">idealr_closed_nontrivial</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed_nontrivial"><span class="id" title="lemma">:</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed_nontrivial"><span class="id" title="lemma">idealr_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed_nontrivial"><span class="id" title="lemma">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr_closed_nontrivial"><span class="id" title="lemma">proper_ideal</span></a>.<br/> <br/> -<span class="id" title="keyword">Structure</span> <a name="idealr"><span class="id" title="record">idealr</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) := <a name="MkIdeal"><span class="id" title="constructor">MkIdeal</span></a> {<br/> +<span class="id" title="keyword">Structure</span> <a name="idealr"><span class="id" title="record">idealr</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) := <a name="MkIdeal"><span class="id" title="constructor">MkIdeal</span></a> {<br/> <a name="idealr_zmod"><span class="id" title="projection">idealr_zmod</span></a> :> <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmodPred"><span class="id" title="abbreviation">zmodPred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a>;<br/> <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#proper_ideal"><span class="id" title="definition">proper_ideal</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><br/> }.<br/> <br/> -<span class="id" title="keyword">Structure</span> <a name="prime_idealr"><span class="id" title="record">prime_idealr</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) := <a name="MkPrimeIdeal"><span class="id" title="constructor">MkPrimeIdeal</span></a> {<br/> +<span class="id" title="keyword">Structure</span> <a name="prime_idealr"><span class="id" title="record">prime_idealr</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">S</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) := <a name="MkPrimeIdeal"><span class="id" title="constructor">MkPrimeIdeal</span></a> {<br/> <a name="prime_idealr_zmod"><span class="id" title="projection">prime_idealr_zmod</span></a> :> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr"><span class="id" title="record">idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a>;<br/> <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#prime_idealr_closed"><span class="id" title="definition">prime_idealr_closed</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#S"><span class="id" title="variable">S</span></a><br/> }.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="Idealr"><span class="id" title="definition">Idealr</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">I</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>) (<span class="id" title="var">zmodI</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmodPred"><span class="id" title="abbreviation">zmodPred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>)<br/> - (<span class="id" title="var">kI</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodI"><span class="id" title="variable">zmodI</span></a>) : <a class="idref" href="mathcomp.algebra.ring_quotient.html#proper_ideal"><span class="id" title="definition">proper_ideal</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr"><span class="id" title="record">idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Idealr"><span class="id" title="definition">Idealr</span></a> (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Ring.Exports.ringType"><span class="id" title="abbreviation">ringType</span></a>) (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">zmodI</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmodPred"><span class="id" title="abbreviation">zmodPred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>)<br/> + (<span class="id" title="var">kI</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodI"><span class="id" title="variable">zmodI</span></a>) : <a class="idref" href="mathcomp.algebra.ring_quotient.html#proper_ideal"><span class="id" title="definition">proper_ideal</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr"><span class="id" title="record">idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>.<br/> <br/> <span class="id" title="keyword">Section</span> <a name="IdealDef.IdealTheory"><span class="id" title="section">IdealTheory</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="IdealDef.IdealTheory.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>) (<a name="IdealDef.IdealTheory.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>)<br/> - (<a name="IdealDef.IdealTheory.idealrI"><span class="id" title="variable">idealrI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr"><span class="id" title="record">idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealrI"><span class="id" title="variable">idealrI</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="IdealDef.IdealTheory.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>) (<a name="IdealDef.IdealTheory.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>)<br/> + (<a name="IdealDef.IdealTheory.idealrI"><span class="id" title="variable">idealrI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr"><span class="id" title="record">idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealrI"><span class="id" title="variable">idealrI</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="idealr1"><span class="id" title="lemma">idealr1</span></a> : 1 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="idealr1"><span class="id" title="lemma">idealr1</span></a> : 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="idealMr"><span class="id" title="lemma">idealMr</span></a> <span class="id" title="var">a</span> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="idealMr"><span class="id" title="lemma">idealMr</span></a> <span class="id" title="var">a</span> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</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.ring_quotient.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="idealr0"><span class="id" title="lemma">idealr0</span></a> : 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="idealr0"><span class="id" title="lemma">idealr0</span></a> : 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory.kI"><span class="id" title="variable">kI</span></a>. <br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.IdealTheory"><span class="id" title="section">IdealTheory</span></a>.<br/> @@ -578,11 +576,11 @@ <span class="id" title="keyword">Section</span> <a name="IdealDef.PrimeIdealTheory"><span class="id" title="section">PrimeIdealTheory</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="IdealDef.PrimeIdealTheory.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Exports.comRingType"><span class="id" title="abbreviation">comRingType</span></a>) (<a name="IdealDef.PrimeIdealTheory.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>)<br/> - (<a name="IdealDef.PrimeIdealTheory.pidealrI"><span class="id" title="variable">pidealrI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#prime_idealr"><span class="id" title="record">prime_idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#pidealrI"><span class="id" title="variable">pidealrI</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="IdealDef.PrimeIdealTheory.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Exports.comRingType"><span class="id" title="abbreviation">comRingType</span></a>) (<a name="IdealDef.PrimeIdealTheory.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>)<br/> + (<a name="IdealDef.PrimeIdealTheory.pidealrI"><span class="id" title="variable">pidealrI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#prime_idealr"><span class="id" title="record">prime_idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#pidealrI"><span class="id" title="variable">pidealrI</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="prime_idealrM"><span class="id" title="lemma">prime_idealrM</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="prime_idealrM"><span class="id" title="lemma">prime_idealrM</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.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.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.PrimeIdealTheory.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#IdealDef.PrimeIdealTheory"><span class="id" title="section">PrimeIdealTheory</span></a>.<br/> @@ -593,14 +591,14 @@ <br/> <span class="id" title="keyword">Module</span> <a name="Quotient"><span class="id" title="module">Quotient</span></a>.<br/> <span class="id" title="keyword">Section</span> <a name="Quotient.ZmodQuotient"><span class="id" title="section">ZmodQuotient</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="Quotient.ZmodQuotient.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.zmodType"><span class="id" title="abbreviation">zmodType</span></a>) (<a name="Quotient.ZmodQuotient.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>)<br/> - (<a name="Quotient.ZmodQuotient.zmodI"><span class="id" title="variable">zmodI</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmodPred"><span class="id" title="abbreviation">zmodPred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodI"><span class="id" title="variable">zmodI</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="Quotient.ZmodQuotient.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.zmodType"><span class="id" title="abbreviation">zmodType</span></a>) (<a name="Quotient.ZmodQuotient.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>)<br/> + (<a name="Quotient.ZmodQuotient.zmodI"><span class="id" title="variable">zmodI</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Pred.Exports.zmodPred"><span class="id" title="abbreviation">zmodPred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#zmodI"><span class="id" title="variable">zmodI</span></a>).<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.equiv"><span class="id" title="definition">equiv</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.R"><span class="id" title="variable">R</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d70623330b2787db6b196e37db7d8f45"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.equiv"><span class="id" title="definition">equiv</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.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#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.equivE"><span class="id" title="lemma">equivE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d70623330b2787db6b196e37db7d8f45"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>. <br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.equivE"><span class="id" title="lemma">equivE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>. <br/> <br/> <span class="id" title="keyword">Lemma</span> <a name="Quotient.equiv_is_equiv"><span class="id" title="lemma">equiv_is_equiv</span></a> : <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#equiv_class_of"><span class="id" title="inductive">equiv_class_of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a>.<br/> @@ -610,99 +608,99 @@ <span class="id" title="keyword">Canonical</span> <span class="id" title="var">equiv_encModRel</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#defaultEncModRel"><span class="id" title="definition">defaultEncModRel</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.type"><span class="id" title="definition">type</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#73f0d3e79bf803b4c740bbb9fa38aa76"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#73f0d3e79bf803b4c740bbb9fa38aa76"><span class="id" title="notation">eq_quot</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#73f0d3e79bf803b4c740bbb9fa38aa76"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.type_of"><span class="id" title="definition">type_of</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.R"><span class="id" title="variable">R</span></a> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.type"><span class="id" title="definition">type</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#0dc587318a1236d89082bca629a5db9b"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#0dc587318a1236d89082bca629a5db9b"><span class="id" title="notation">eq_quot</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#0dc587318a1236d89082bca629a5db9b"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.type_of"><span class="id" title="definition">type_of</span></a> <span class="id" title="keyword">of</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.ring_quotient.html#Quotient.ZmodQuotient.R"><span class="id" title="variable">R</span></a> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a>.<br/> <br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_quotType</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#a70f324fea4d80f55c2255a07c19c5c5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#a70f324fea4d80f55c2255a07c19c5c5"><span class="id" title="notation">quotType</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#a70f324fea4d80f55c2255a07c19c5c5"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#a70f324fea4d80f55c2255a07c19c5c5"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_eqType</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">eqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_choiceType</span> := <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">choiceType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#1731a28227324c9e5fc49499029635b3"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_eqQuotType</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#b7a0622a915c3e5a7396a3208b40639a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#b7a0622a915c3e5a7396a3208b40639a"><span class="id" title="notation">eqQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#b7a0622a915c3e5a7396a3208b40639a"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#b7a0622a915c3e5a7396a3208b40639a"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_quotType</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#2b6ecaeff71b4103d20b05dbc196dba6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#2b6ecaeff71b4103d20b05dbc196dba6"><span class="id" title="notation">quotType</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#2b6ecaeff71b4103d20b05dbc196dba6"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#2b6ecaeff71b4103d20b05dbc196dba6"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_eqType</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">eqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_choiceType</span> := <a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">choiceType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">]</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_eqQuotType</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#dc3d569865bd181e003ea2b17400befd"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#dc3d569865bd181e003ea2b17400befd"><span class="id" title="notation">eqQuotType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.equiv"><span class="id" title="definition">equiv</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#dc3d569865bd181e003ea2b17400befd"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#dc3d569865bd181e003ea2b17400befd"><span class="id" title="notation">]</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.idealrBE"><span class="id" title="lemma">idealrBE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d70623330b2787db6b196e37db7d8f45"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.idealrBE"><span class="id" title="lemma">idealrBE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.idealrDE"><span class="id" title="lemma">idealrDE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#ae4d81913e6239182a9ac7467ffde8cd"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.idealrDE"><span class="id" title="lemma">idealrDE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.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.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient.kI"><span class="id" title="variable">kI</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><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.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="Quotient.zero"><span class="id" title="definition">zero</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_cst"><span class="id" title="abbreviation">lift_cst</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> 0.<br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.add"><span class="id" title="definition">add</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_op2"><span class="id" title="abbreviation">lift_op2</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">R</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.opp"><span class="id" title="definition">opp</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_op1"><span class="id" title="abbreviation">lift_op1</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">R</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.add"><span class="id" title="definition">add</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_op2"><span class="id" title="abbreviation">lift_op2</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">R</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.opp"><span class="id" title="definition">opp</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_op1"><span class="id" title="abbreviation">lift_op1</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">R</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_zero_morph</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiConst"><span class="id" title="abbreviation">PiConst</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.zero"><span class="id" title="definition">zero</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.pi_opp"><span class="id" title="lemma">pi_opp</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f090f187f28139994197271ddc594c91"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f090f187f28139994197271ddc594c91"><span class="id" title="notation">pi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.opp"><span class="id" title="definition">opp</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#59b5bb4add86e1e9ecbe874e74b2216e"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.pi_opp"><span class="id" title="lemma">pi_opp</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c3fdc30b5d212c820acf98356210d6f7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c3fdc30b5d212c820acf98356210d6f7"><span class="id" title="notation">pi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">:</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#8bf6fdbe8b0c22b67e58fa5cd9937190"><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.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.opp"><span class="id" title="definition">opp</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#8bf6fdbe8b0c22b67e58fa5cd9937190"><span class="id" title="notation">}</span></a>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_opp_morph</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiMorph1"><span class="id" title="abbreviation">PiMorph1</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_opp"><span class="id" title="lemma">pi_opp</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.pi_add"><span class="id" title="lemma">pi_add</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f090f187f28139994197271ddc594c91"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f090f187f28139994197271ddc594c91"><span class="id" title="notation">pi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#ae4d81913e6239182a9ac7467ffde8cd"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.pi_add"><span class="id" title="lemma">pi_add</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c3fdc30b5d212c820acf98356210d6f7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c3fdc30b5d212c820acf98356210d6f7"><span class="id" title="notation">pi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a>.<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_add_morph</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiMorph2"><span class="id" title="abbreviation">PiMorph2</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_add"><span class="id" title="lemma">pi_add</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.addqA"><span class="id" title="lemma">addqA</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#associative"><span class="id" title="definition">associative</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.addqA"><span class="id" title="lemma">addqA</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.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.addqC"><span class="id" title="lemma">addqC</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.addqC"><span class="id" title="lemma">addqC</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.add0q"><span class="id" title="lemma">add0q</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.zero"><span class="id" title="definition">zero</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.add0q"><span class="id" title="lemma">add0q</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.ring_quotient.html#Quotient.zero"><span class="id" title="definition">zero</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.addNq"><span class="id" title="lemma">addNq</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#left_inverse"><span class="id" title="definition">left_inverse</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.zero"><span class="id" title="definition">zero</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.opp"><span class="id" title="definition">opp</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.addNq"><span class="id" title="lemma">addNq</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.ring_quotient.html#Quotient.zero"><span class="id" title="definition">zero</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.opp"><span class="id" title="definition">opp</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add"><span class="id" title="definition">add</span></a>.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="Quotient.rquot_zmodMixin"><span class="id" title="definition">rquot_zmodMixin</span></a> := <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.Zmodule.Exports.ZmodMixin"><span class="id" title="abbreviation">ZmodMixin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.addqA"><span class="id" title="lemma">addqA</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.addqC"><span class="id" title="lemma">addqC</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.add0q"><span class="id" title="lemma">add0q</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.addNq"><span class="id" title="lemma">addNq</span></a>.<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_zmodType</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.algebra.ssralg.html#GRing.Zmodule.Exports.ZmodType"><span class="id" title="abbreviation">ZmodType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.rquot_zmodMixin"><span class="id" title="definition">rquot_zmodMixin</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.rquot_zmodQuotMixin"><span class="id" title="definition">rquot_zmodQuotMixin</span></a> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotMixin"><span class="id" title="abbreviation">ZmodQuotMixin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#lock"><span class="id" title="lemma">lock</span></a> <span class="id" title="var">_</span>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_opp"><span class="id" title="lemma">pi_opp</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_add"><span class="id" title="lemma">pi_add</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_zmodQuotType</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotType"><span class="id" title="abbreviation">ZmodQuotType</span></a> 0 <a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#9fdf1a446ceec36bc97cce801a3ef3f2"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.rquot_zmodQuotMixin"><span class="id" title="definition">rquot_zmodQuotMixin</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.rquot_zmodQuotMixin"><span class="id" title="definition">rquot_zmodQuotMixin</span></a> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotMixin"><span class="id" title="abbreviation">ZmodQuotMixin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#lock"><span class="id" title="lemma">lock</span></a> <span class="id" title="var">_</span>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_opp"><span class="id" title="lemma">pi_opp</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_add"><span class="id" title="lemma">pi_add</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_zmodQuotType</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#ZmodQuotType"><span class="id" title="abbreviation">ZmodQuotType</span></a> 0 <a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="definition">type</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.rquot_zmodQuotMixin"><span class="id" title="definition">rquot_zmodQuotMixin</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.ZmodQuotient"><span class="id" title="section">ZmodQuotient</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="88169e749a9591eb9f0672e6db2adc1d"><span class="id" title="notation">"</span></a>{quot I }" := (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type_of"><span class="id" title="definition">type_of</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">I</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">_</span>)).<br/> +<span class="id" title="keyword">Notation</span> <a name="a6fe06a691395e8325c45837ef0fd549"><span class="id" title="notation">"</span></a>{quot I }" := (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type_of"><span class="id" title="definition">type_of</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">I</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">_</span>)).<br/> <br/> <span class="id" title="keyword">Section</span> <a name="Quotient.RingQuotient"><span class="id" title="section">RingQuotient</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="Quotient.RingQuotient.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Exports.comRingType"><span class="id" title="abbreviation">comRingType</span></a>) (<a name="Quotient.RingQuotient.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>)<br/> - (<a name="Quotient.RingQuotient.idealI"><span class="id" title="variable">idealI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr"><span class="id" title="record">idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="Quotient.RingQuotient.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealI"><span class="id" title="variable">idealI</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="Quotient.RingQuotient.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Exports.comRingType"><span class="id" title="abbreviation">comRingType</span></a>) (<a name="Quotient.RingQuotient.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>)<br/> + (<a name="Quotient.RingQuotient.idealI"><span class="id" title="variable">idealI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealr"><span class="id" title="record">idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="Quotient.RingQuotient.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#idealI"><span class="id" title="variable">idealI</span></a>).<br/> <br/> <br/> <span class="id" title="keyword">Definition</span> <a name="Quotient.one"><span class="id" title="definition">one</span></a>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_cst"><span class="id" title="abbreviation">lift_cst</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> 1.<br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.mul"><span class="id" title="definition">mul</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_op2"><span class="id" title="abbreviation">lift_op2</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#d5d4e2467843f67554f1a8a22d125de9"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#d5d4e2467843f67554f1a8a22d125de9"><span class="id" title="notation">R</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.mul"><span class="id" title="definition">mul</span></a> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#lift_op2"><span class="id" title="abbreviation">lift_op2</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</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>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_one_morph</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiConst"><span class="id" title="abbreviation">PiConst</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.one"><span class="id" title="definition">one</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.pi_mul"><span class="id" title="lemma">pi_mul</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f090f187f28139994197271ddc594c91"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f090f187f28139994197271ddc594c91"><span class="id" title="notation">pi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#a0fd72584f326d7220475d01d3fceccd"><span class="id" title="notation">}</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.pi_mul"><span class="id" title="lemma">pi_mul</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c3fdc30b5d212c820acf98356210d6f7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c3fdc30b5d212c820acf98356210d6f7"><span class="id" title="notation">pi</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.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.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a>.<br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">pi_mul_morph</span> := <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#PiMorph2"><span class="id" title="abbreviation">PiMorph2</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_mul"><span class="id" title="lemma">pi_mul</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.mulqA"><span class="id" title="lemma">mulqA</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#associative"><span class="id" title="definition">associative</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.mulqA"><span class="id" title="lemma">mulqA</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.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.mulqC"><span class="id" title="lemma">mulqC</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.mulqC"><span class="id" title="lemma">mulqC</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.mul1q"><span class="id" title="lemma">mul1q</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.one"><span class="id" title="definition">one</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.mul1q"><span class="id" title="lemma">mul1q</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.ring_quotient.html#Quotient.one"><span class="id" title="definition">one</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.mulq_addl"><span class="id" title="lemma">mulq_addl</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#left_distributive"><span class="id" title="definition">left_distributive</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#327bb2f0da6fd7c01a004dedcfc2dee4"><span class="id" title="notation">R</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.mulq_addl"><span class="id" title="lemma">mulq_addl</span></a>: <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_distributive"><span class="id" title="definition">left_distributive</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mul"><span class="id" title="definition">mul</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">R</span></a>.<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.nonzero1q"><span class="id" title="lemma">nonzero1q</span></a>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.one"><span class="id" title="definition">one</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> 0.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.nonzero1q"><span class="id" title="lemma">nonzero1q</span></a>: <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.one"><span class="id" title="definition">one</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> 0.<br/> <br/> <span class="id" title="keyword">Definition</span> <a name="Quotient.rquot_comRingMixin"><span class="id" title="definition">rquot_comRingMixin</span></a> :=<br/> @@ -713,8 +711,8 @@ <span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_comRingType</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.algebra.ssralg.html#GRing.ComRing.Exports.ComRingType"><span class="id" title="abbreviation">ComRingType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.mulqC"><span class="id" title="lemma">mulqC</span></a>.<br/> <br/> -<span class="id" title="keyword">Definition</span> <a name="Quotient.rquot_ringQuotMixin"><span class="id" title="definition">rquot_ringQuotMixin</span></a> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotMixin"><span class="id" title="abbreviation">RingQuotMixin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#lock"><span class="id" title="lemma">lock</span></a> <span class="id" title="var">_</span>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_mul"><span class="id" title="lemma">pi_mul</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_ringQuotType</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotType"><span class="id" title="abbreviation">RingQuotType</span></a> 1 <a class="idref" href="mathcomp.algebra.ssralg.html#d5d4e2467843f67554f1a8a22d125de9"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#d5d4e2467843f67554f1a8a22d125de9"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.rquot_ringQuotMixin"><span class="id" title="definition">rquot_ringQuotMixin</span></a>.<br/> +<span class="id" title="keyword">Definition</span> <a name="Quotient.rquot_ringQuotMixin"><span class="id" title="definition">rquot_ringQuotMixin</span></a> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotMixin"><span class="id" title="abbreviation">RingQuotMixin</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#lock"><span class="id" title="lemma">lock</span></a> <span class="id" title="var">_</span>) <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.pi_mul"><span class="id" title="lemma">pi_mul</span></a>.<br/> +<span class="id" title="keyword">Canonical</span> <span class="id" title="var">rquot_ringQuotType</span> := <a class="idref" href="mathcomp.algebra.ring_quotient.html#RingQuotType"><span class="id" title="abbreviation">RingQuotType</span></a> 1 <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="mathcomp.algebra.ring_quotient.html#Quotient.type"><span class="id" title="abbreviation">type</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.rquot_ringQuotMixin"><span class="id" title="definition">rquot_ringQuotMixin</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.RingQuotient"><span class="id" title="section">RingQuotient</span></a>.<br/> @@ -723,11 +721,11 @@ <span class="id" title="keyword">Section</span> <a name="Quotient.IDomainQuotient"><span class="id" title="section">IDomainQuotient</span></a>.<br/> <br/> -<span class="id" title="keyword">Variables</span> (<a name="Quotient.IDomainQuotient.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Exports.comRingType"><span class="id" title="abbreviation">comRingType</span></a>) (<a name="Quotient.IDomainQuotient.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a>)<br/> - (<a name="Quotient.IDomainQuotient.pidealI"><span class="id" title="variable">pidealI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#prime_idealr"><span class="id" title="record">prime_idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="Quotient.IDomainQuotient.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#pidealI"><span class="id" title="variable">pidealI</span></a>).<br/> +<span class="id" title="keyword">Variables</span> (<a name="Quotient.IDomainQuotient.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssralg.html#GRing.ComRing.Exports.comRingType"><span class="id" title="abbreviation">comRingType</span></a>) (<a name="Quotient.IDomainQuotient.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>)<br/> + (<a name="Quotient.IDomainQuotient.pidealI"><span class="id" title="variable">pidealI</span></a> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#prime_idealr"><span class="id" title="record">prime_idealr</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#I"><span class="id" title="variable">I</span></a>) (<a name="Quotient.IDomainQuotient.kI"><span class="id" title="variable">kI</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#keyed_pred"><span class="id" title="record">keyed_pred</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#pidealI"><span class="id" title="variable">pidealI</span></a>).<br/> <br/> -<span class="id" title="keyword">Lemma</span> <a name="Quotient.rquot_IdomainAxiom"><span class="id" title="lemma">rquot_IdomainAxiom</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#88169e749a9591eb9f0672e6db2adc1d"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#88169e749a9591eb9f0672e6db2adc1d"><span class="id" title="notation">quot</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.IDomainQuotient.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#88169e749a9591eb9f0672e6db2adc1d"><span class="id" title="notation">}</span></a>): <a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#22058a36a53dac65c94ca403bc62650a"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a>.<br/> +<span class="id" title="keyword">Lemma</span> <a name="Quotient.rquot_IdomainAxiom"><span class="id" title="lemma">rquot_IdomainAxiom</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.ring_quotient.html#a6fe06a691395e8325c45837ef0fd549"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#a6fe06a691395e8325c45837ef0fd549"><span class="id" title="notation">quot</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.IDomainQuotient.kI"><span class="id" title="variable">kI</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#a6fe06a691395e8325c45837ef0fd549"><span class="id" title="notation">}</span></a>): <a class="idref" href="mathcomp.algebra.ring_quotient.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.ring_quotient.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> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="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.ring_quotient.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> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 0<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> <br/> <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient.IDomainQuotient"><span class="id" title="section">IDomainQuotient</span></a>.<br/> @@ -736,15 +734,15 @@ <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.ring_quotient.html#Quotient"><span class="id" title="module">Quotient</span></a>.<br/> <br/> -<span class="id" title="keyword">Notation</span> <a name="5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">"</span></a>{ideal_quot I }" := (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#type_of"><span class="id" title="definition">Quotient.type_of</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">I</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">_</span>)).<br/> -<span class="id" title="keyword">Notation</span> <a name="196067f7d6bffa40cbf887ea96632cdc"><span class="id" title="notation">"</span></a>x == y %[mod_ideal I ]" :=<br/> - (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#433801266bfe38f0ebd6037860203596"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c859a47d820a24af55974b4566666a01"><span class="id" title="notation">"</span></a>x = y %[mod_ideal I ]" :=<br/> - (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#1d0bea61314a6549a966f59a90fca2c5"><span class="id" title="notation">=</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#1d0bea61314a6549a966f59a90fca2c5"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#1d0bea61314a6549a966f59a90fca2c5"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#1d0bea61314a6549a966f59a90fca2c5"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="cd4535596c25d791de7da2f2f60c5a5e"><span class="id" title="notation">"</span></a>x != y %[mod_ideal I ]" :=<br/> - (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#64dce3fc11e63c73e37431825b6bda70"><span class="id" title="notation">!=</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#64dce3fc11e63c73e37431825b6bda70"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#64dce3fc11e63c73e37431825b6bda70"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#64dce3fc11e63c73e37431825b6bda70"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="879ec6e7c966bcda09371cc771e11f08"><span class="id" title="notation">"</span></a>x <> y %[mod_ideal I ]" :=<br/> - (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c19d82d8c4200cd8b2206f1641e1d5ca"><span class="id" title="notation">≠</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c19d82d8c4200cd8b2206f1641e1d5ca"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c19d82d8c4200cd8b2206f1641e1d5ca"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#5eedbcbd3de3491e3e0645ec1f0ac7aa"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#c19d82d8c4200cd8b2206f1641e1d5ca"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">"</span></a>{ideal_quot I }" := (@<a class="idref" href="mathcomp.algebra.ring_quotient.html#type_of"><span class="id" title="definition">Quotient.type_of</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">I</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">_</span>)).<br/> +<span class="id" title="keyword">Notation</span> <a name="e7ee8f56dce7b7542abca76562f46e1a"><span class="id" title="notation">"</span></a>x == y %[mod_ideal I ]" :=<br/> + (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#e3392789fbfaf247c0fb823980d6e8ff"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="003cf0caf973207d33de5c02ff3f947b"><span class="id" title="notation">"</span></a>x = y %[mod_ideal I ]" :=<br/> + (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f562cbd652d1fe79fbd8d329b05b5257"><span class="id" title="notation">=</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f562cbd652d1fe79fbd8d329b05b5257"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f562cbd652d1fe79fbd8d329b05b5257"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#f562cbd652d1fe79fbd8d329b05b5257"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="8736f16c8ea8178eb63cf34c29faa11c"><span class="id" title="notation">"</span></a>x != y %[mod_ideal I ]" :=<br/> + (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#9a82670521214c5e7453279f44112385"><span class="id" title="notation">!=</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#9a82670521214c5e7453279f44112385"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#9a82670521214c5e7453279f44112385"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#9a82670521214c5e7453279f44112385"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> +<span class="id" title="keyword">Notation</span> <a name="8e198f937f9fe8f6b608a05a6be80be9"><span class="id" title="notation">"</span></a>x <> y %[mod_ideal I ]" :=<br/> + (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#fa232142435a5045b9ecd83984a98dc6"><span class="id" title="notation">≠</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.generic_quotient.html#fa232142435a5045b9ecd83984a98dc6"><span class="id" title="notation">%[</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#fa232142435a5045b9ecd83984a98dc6"><span class="id" title="notation">mod</span></a> <a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">ideal_quot</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.algebra.ring_quotient.html#b7e4ed42194c62b5f70715d308bee471"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.generic_quotient.html#fa232142435a5045b9ecd83984a98dc6"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">quotient_scope</span>.<br/> <br/> <span class="id" title="keyword">Canonical</span> <span class="id" title="var">Quotient.rquot_eqType</span>.<br/> |