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| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> | ||
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| <a href="../">Project Page</a> | ||
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| <div id="content" tabindex="-1" onblur="document.getElementById('content').focus()"> | ||
| <div id="main"> | ||
| <h1 class="libtitle">WiSE.equalities</h1> | ||
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| <a id="lab1"></a><h1 class="section">Types With Equalities</h1> | ||
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| <div class="code"> | ||
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| <span class="id" title="keyword">Class</span> <a id="Eq" class="idref" href="#Eq"><span class="id" title="record">Eq</span></a> (<a id="A:1" class="idref" href="#A:1"><span class="id" title="binder">A</span></a> : <span class="id" title="keyword">Type</span>) := <a id="EQ" class="idref" href="#EQ"><span class="id" title="constructor">EQ</span></a> {<br/> | ||
| <a id="eq_op" class="idref" href="#eq_op"><span class="id" title="projection">eq_op</span></a> : <a class="idref" href="WiSE.equalities.html#A:1"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="WiSE.equalities.html#A:1"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <span class="id" title="keyword">Prop</span>;<br/> | ||
| }.<br/> | ||
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| <span class="id" title="keyword">Infix</span> <a id="8f9238d4eefe0b5c60a6c98165047666" class="idref" href="#8f9238d4eefe0b5c60a6c98165047666"><span class="id" title="notation">"</span></a>≡" := <a class="idref" href="WiSE.equalities.html#eq_op"><span class="id" title="method">eq_op</span></a> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 80).<br/> | ||
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| <span class="id" title="keyword">Definition</span> <a id="bijection" class="idref" href="#bijection"><span class="id" title="definition">bijection</span></a> (<a id="A:4" class="idref" href="#A:4"><span class="id" title="binder">A</span></a> <a id="B:5" class="idref" href="#B:5"><span class="id" title="binder">B</span></a> : <span class="id" title="keyword">Type</span>) `{<a id="H:6" class="idref" href="#H:6"><span class="id" title="binder">Eq</span></a> <a id="H:6" class="idref" href="#H:6"><span class="id" title="binder">A</span></a>} `{<a id="H0:7" class="idref" href="#H0:7"><span class="id" title="binder">Eq</span></a> <a id="H0:7" class="idref" href="#H0:7"><span class="id" title="binder">B</span></a>} (<a id="f:8" class="idref" href="#f:8"><span class="id" title="binder">f</span></a> : <a class="idref" href="WiSE.equalities.html#A:4"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="WiSE.equalities.html#B:5"><span class="id" title="variable">B</span></a>) (<a id="g:9" class="idref" href="#g:9"><span class="id" title="binder">g</span></a> : <a class="idref" href="WiSE.equalities.html#B:5"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="WiSE.equalities.html#A:4"><span class="id" title="variable">A</span></a>) :=<br/> | ||
| <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">(</span></a><span class="id" title="keyword">forall</span> <a id="a:10" class="idref" href="#a:10"><span class="id" title="binder">a</span></a>, <a class="idref" href="WiSE.equalities.html#g:9"><span class="id" title="variable">g</span></a> (<a class="idref" href="WiSE.equalities.html#f:8"><span class="id" title="variable">f</span></a> <a class="idref" href="WiSE.equalities.html#a:10"><span class="id" title="variable">a</span></a>) <a class="idref" href="WiSE.equalities.html#8f9238d4eefe0b5c60a6c98165047666"><span class="id" title="notation">≡</span></a> <a class="idref" href="WiSE.equalities.html#a:10"><span class="id" title="variable">a</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">/\</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">(</span></a><span class="id" title="keyword">forall</span> <a id="b:11" class="idref" href="#b:11"><span class="id" title="binder">b</span></a>, <a class="idref" href="WiSE.equalities.html#f:8"><span class="id" title="variable">f</span></a> (<a class="idref" href="WiSE.equalities.html#g:9"><span class="id" title="variable">g</span></a> <a class="idref" href="WiSE.equalities.html#b:11"><span class="id" title="variable">b</span></a>) <a class="idref" href="WiSE.equalities.html#8f9238d4eefe0b5c60a6c98165047666"><span class="id" title="notation">≡</span></a> <a class="idref" href="WiSE.equalities.html#b:11"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">)</span></a>.<br/> | ||
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| <span class="id" title="keyword">Definition</span> <a id="isomorph" class="idref" href="#isomorph"><span class="id" title="definition">isomorph</span></a> (<a id="A:12" class="idref" href="#A:12"><span class="id" title="binder">A</span></a> <a id="B:13" class="idref" href="#B:13"><span class="id" title="binder">B</span></a> : <span class="id" title="keyword">Type</span>) `{<a id="H:14" class="idref" href="#H:14"><span class="id" title="binder">Eq</span></a> <a id="H:14" class="idref" href="#H:14"><span class="id" title="binder">A</span></a>} `{<a id="H0:15" class="idref" href="#H0:15"><span class="id" title="binder">Eq</span></a> <a id="H0:15" class="idref" href="#H0:15"><span class="id" title="binder">B</span></a>} :=<br/> | ||
| <a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">exists</span></a> <a id="f:16" class="idref" href="#f:16"><span class="id" title="binder">f</span></a> <a id="g:17" class="idref" href="#g:17"><span class="id" title="binder">g</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.13.2/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="WiSE.equalities.html#bijection"><span class="id" title="definition">bijection</span></a> <a class="idref" href="WiSE.equalities.html#A:12"><span class="id" title="variable">A</span></a> <a class="idref" href="WiSE.equalities.html#B:13"><span class="id" title="variable">B</span></a> <a class="idref" href="WiSE.equalities.html#f:16"><span class="id" title="variable">f</span></a> <a class="idref" href="WiSE.equalities.html#g:17"><span class="id" title="variable">g</span></a>.<br/> | ||
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| <span class="id" title="keyword">Infix</span> <a id="47ab0ac71cf2dac51fa901d3dcced8db" class="idref" href="#47ab0ac71cf2dac51fa901d3dcced8db"><span class="id" title="notation">"</span></a>≃" := <a class="idref" href="WiSE.equalities.html#isomorph"><span class="id" title="definition">isomorph</span></a> (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 80).<br/> | ||
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