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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link href="coqdoc.css" rel="stylesheet" type="text/css" />
<title>coqrel.BoolRel</title>
</head>
<body>
<div id="page">
<div id="header">
</div>
<div id="main">
<h1 class="libtitle">Library coqrel.BoolRel</h1>
<div class="code">
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="coqrel.LogicalRelations.html#"><span class="id" title="library">LogicalRelations</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Export</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#"><span class="id" title="library">Coq.Bool.Bool</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab455"></a><h1 class="section">Relations for <span class="inlinecode"><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#sumbool"><span class="id" title="inductive">sumbool</span></a></span></h1>
<div class="paragraph"> </div>
<a name="lab456"></a><h2 class="section">Symmetric relation</h2>
<div class="paragraph"> </div>
NB: With proof irrelevance this is the same as <span class="inlinecode"><a class="idref" href="compcert.x86.Asm.html#PregEq.eq"><span class="id" title="definition">eq</span></a></span>.
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Inductive</span> <a name="sumbool_rel"><span class="id" title="inductive">sumbool_rel</span></a> {<span class="id" title="var">P1</span> <span class="id" title="var">P2</span> <span class="id" title="var">Q1</span> <span class="id" title="var">Q2</span>}: <a class="idref" href="coqrel.RelDefinitions.html#rel"><span class="id" title="definition">rel</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#sumbool"><span class="id" title="inductive">sumbool</span></a> <span class="id" title="var">P1</span> <span class="id" title="var">Q1</span>) (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#sumbool"><span class="id" title="inductive">sumbool</span></a> <span class="id" title="var">P2</span> <span class="id" title="var">Q2</span>):=<br/>
| <a name="left_rel_def"><span class="id" title="constructor">left_rel_def</span></a> <span class="id" title="var">H1</span> <span class="id" title="var">H2</span>: <a class="idref" href="coqrel.BoolRel.html#sumbool_rel"><span class="id" title="inductive">sumbool_rel</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#left"><span class="id" title="constructor">left</span></a> <a class="idref" href="coqrel.BoolRel.html#H1"><span class="id" title="variable">H1</span></a>) (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#left"><span class="id" title="constructor">left</span></a> <a class="idref" href="coqrel.BoolRel.html#H2"><span class="id" title="variable">H2</span></a>)<br/>
| <a name="right_rel_def"><span class="id" title="constructor">right_rel_def</span></a> <span class="id" title="var">H1</span> <span class="id" title="var">H2</span>: <a class="idref" href="coqrel.BoolRel.html#sumbool_rel"><span class="id" title="inductive">sumbool_rel</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#right"><span class="id" title="constructor">right</span></a> <a class="idref" href="coqrel.BoolRel.html#H1"><span class="id" title="variable">H1</span></a>) (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#right"><span class="id" title="constructor">right</span></a> <a class="idref" href="coqrel.BoolRel.html#H2"><span class="id" title="variable">H2</span></a>).<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="left_rel"><span class="id" title="instance">left_rel</span></a>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Monotonic"><span class="id" title="abbreviation">Monotonic</span></a> (@<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#left"><span class="id" title="constructor">left</span></a>) (<a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">forallr</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">:</span></a> <a class="idref" href="coqrel.RelOperators.html#2ba22b4c3fc52a802af99bc58fee3c46"><span class="id" title="notation">⊤</span></a><a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">,</span></a> <a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">forallr</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">:</span></a> <a class="idref" href="coqrel.RelOperators.html#2ba22b4c3fc52a802af99bc58fee3c46"><span class="id" title="notation">⊤</span></a><a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">,</span></a> <a class="idref" href="coqrel.RelOperators.html#2ba22b4c3fc52a802af99bc58fee3c46"><span class="id" title="notation">⊤</span></a> <a class="idref" href="coqrel.RelDefinitions.html#d5d0ad6beccd25d5224442d64ed307d5"><span class="id" title="notation">++></span></a> <a class="idref" href="coqrel.BoolRel.html#sumbool_rel"><span class="id" title="inductive">sumbool_rel</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="right_rel"><span class="id" title="instance">right_rel</span></a>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Monotonic"><span class="id" title="abbreviation">Monotonic</span></a> (@<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#right"><span class="id" title="constructor">right</span></a>) (<a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">forallr</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">:</span></a> <a class="idref" href="coqrel.RelOperators.html#2ba22b4c3fc52a802af99bc58fee3c46"><span class="id" title="notation">⊤</span></a><a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">,</span></a> <a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">forallr</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">:</span></a> <a class="idref" href="coqrel.RelOperators.html#2ba22b4c3fc52a802af99bc58fee3c46"><span class="id" title="notation">⊤</span></a><a class="idref" href="coqrel.Relators.html#4adbc34bd4a36d15cb3084cd06569b08"><span class="id" title="notation">,</span></a> <a class="idref" href="coqrel.RelOperators.html#2ba22b4c3fc52a802af99bc58fee3c46"><span class="id" title="notation">⊤</span></a> <a class="idref" href="coqrel.RelDefinitions.html#d5d0ad6beccd25d5224442d64ed307d5"><span class="id" title="notation">++></span></a> <a class="idref" href="coqrel.BoolRel.html#sumbool_rel"><span class="id" title="inductive">sumbool_rel</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab457"></a><h2 class="section">Directed relation</h2>
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Inductive</span> <a name="sumbool_le"><span class="id" title="inductive">sumbool_le</span></a> {<span class="id" title="var">P1</span> <span class="id" title="var">P2</span> <span class="id" title="var">Q1</span> <span class="id" title="var">Q2</span>}: <a class="idref" href="coqrel.RelDefinitions.html#rel"><span class="id" title="definition">rel</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#sumbool"><span class="id" title="inductive">sumbool</span></a> <span class="id" title="var">P1</span> <span class="id" title="var">Q1</span>) (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#sumbool"><span class="id" title="inductive">sumbool</span></a> <span class="id" title="var">P2</span> <span class="id" title="var">Q2</span>):=<br/>
| <a name="left_le"><span class="id" title="constructor">left_le</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">H2</span>: <a class="idref" href="coqrel.RelDefinitions.html#Related"><span class="id" title="class">Related</span></a> <a class="idref" href="coqrel.BoolRel.html#b1"><span class="id" title="variable">b1</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#left"><span class="id" title="constructor">left</span></a> <a class="idref" href="coqrel.BoolRel.html#H2"><span class="id" title="variable">H2</span></a>) <a class="idref" href="coqrel.BoolRel.html#sumbool_le"><span class="id" title="inductive">sumbool_le</span></a><br/>
| <a name="right_le"><span class="id" title="constructor">right_le</span></a> <span class="id" title="var">H1</span> <span class="id" title="var">b2</span>: <a class="idref" href="coqrel.RelDefinitions.html#Related"><span class="id" title="class">Related</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Specif.html#right"><span class="id" title="constructor">right</span></a> <a class="idref" href="coqrel.BoolRel.html#H1"><span class="id" title="variable">H1</span></a>) <a class="idref" href="coqrel.BoolRel.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="coqrel.BoolRel.html#sumbool_le"><span class="id" title="inductive">sumbool_le</span></a>.<br/>
<br/>
<span class="id" title="keyword">Global</span> <span class="id" title="var">Existing</span> <span class="id" title="keyword">Instance</span> <span class="id" title="var">left_le</span>.<br/>
<span class="id" title="keyword">Global</span> <span class="id" title="var">Existing</span> <span class="id" title="keyword">Instance</span> <span class="id" title="var">right_le</span>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab458"></a><h1 class="section">Definitions for <span class="inlinecode"><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.PArith.BinPos.html#Pos.leb"><span class="id" title="definition">leb</span></a></span></h1>
<div class="paragraph"> </div>
<a name="lab459"></a><h2 class="section">Properties</h2>
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Lemma</span> <a name="leb_rdestruct"><span class="id" title="lemma">leb_rdestruct</span></a>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#RDestruct"><span class="id" title="class">RDestruct</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">P</span> ⇒ <a class="idref" href="coqrel.BoolRel.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a> <a class="idref" href="coqrel.BoolRel.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a> <a class="idref" href="coqrel.BoolRel.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> <span class="id" title="var">Hb</span> <span class="id" title="var">P</span> (<span class="id" title="var">HPff</span> & <span class="id" title="var">HPtt</span> & <span class="id" title="var">HPft</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">b1</span>, <span class="id" title="var">b2</span>; <span class="id" title="tactic">eauto</span>; <span class="id" title="tactic">discriminate</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Hint Extern</span> 0 (<a class="idref" href="coqrel.RelDefinitions.html#RDestruct"><span class="id" title="class">RDestruct</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <span class="id" title="var">_</span>) ⇒<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="coqrel.BoolRel.html#leb_rdestruct"><span class="id" title="lemma">leb_rdestruct</span></a> : <span class="id" title="var">typeclass_instances</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="leb_transport_eq_true"><span class="id" title="instance">leb_transport_eq_true</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span>:<br/>
<a class="idref" href="coqrel.Transport.html#Transport"><span class="id" title="class">Transport</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">Bool.leb</span></a> <a class="idref" href="coqrel.BoolRel.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="coqrel.BoolRel.html#y"><span class="id" title="variable">y</span></a> (<a class="idref" href="coqrel.BoolRel.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a>) (<a class="idref" href="coqrel.BoolRel.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>, <span class="id" title="var">y</span>; <span class="id" title="tactic">firstorder</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab460"></a><h2 class="section">Monotonicity of various definitions</h2>
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Lemma</span> <a name="true_leb"><span class="id" title="lemma">true_leb</span></a> <span class="id" title="var">b</span>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Related"><span class="id" title="class">Related</span></a> <a class="idref" href="coqrel.BoolRel.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">b</span>; <span class="id" title="tactic">reflexivity</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Hint Extern</span> 0 (<a class="idref" href="coqrel.RelDefinitions.html#Related"><span class="id" title="class">Related</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <span class="id" title="var">_</span>) ⇒<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="coqrel.BoolRel.html#true_leb"><span class="id" title="lemma">true_leb</span></a> : <span class="id" title="var">typeclass_instances</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="false_leb"><span class="id" title="lemma">false_leb</span></a> <span class="id" title="var">b</span>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Related"><span class="id" title="class">Related</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="coqrel.BoolRel.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">b</span>; <span class="id" title="tactic">reflexivity</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Hint Extern</span> 0 (<a class="idref" href="coqrel.RelDefinitions.html#Related"><span class="id" title="class">Related</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>) ⇒<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="coqrel.BoolRel.html#false_leb"><span class="id" title="lemma">false_leb</span></a> : <span class="id" title="var">typeclass_instances</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="negb_leb"><span class="id" title="instance">negb_leb</span></a>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Monotonic"><span class="id" title="abbreviation">Monotonic</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#negb"><span class="id" title="definition">negb</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <a class="idref" href="coqrel.RelDefinitions.html#28fb2fb3952fac7e01eb907871e1ea99"><span class="id" title="notation">--></span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#negb"><span class="id" title="definition">negb</span></a>.<br/>
<span class="id" title="var">rauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="andb_leb"><span class="id" title="instance">andb_leb</span></a>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Monotonic"><span class="id" title="abbreviation">Monotonic</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#andb"><span class="id" title="definition">andb</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <a class="idref" href="coqrel.RelDefinitions.html#d5d0ad6beccd25d5224442d64ed307d5"><span class="id" title="notation">++></span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <a class="idref" href="coqrel.RelDefinitions.html#d5d0ad6beccd25d5224442d64ed307d5"><span class="id" title="notation">++></span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#andb"><span class="id" title="definition">andb</span></a>.<br/>
<span class="id" title="var">rauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="orb_leb"><span class="id" title="instance">orb_leb</span></a>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Monotonic"><span class="id" title="abbreviation">Monotonic</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#orb"><span class="id" title="definition">orb</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <a class="idref" href="coqrel.RelDefinitions.html#d5d0ad6beccd25d5224442d64ed307d5"><span class="id" title="notation">++></span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <a class="idref" href="coqrel.RelDefinitions.html#d5d0ad6beccd25d5224442d64ed307d5"><span class="id" title="notation">++></span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#orb"><span class="id" title="definition">orb</span></a>.<br/>
<span class="id" title="var">rauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="implb_leb"><span class="id" title="instance">implb_leb</span></a>:<br/>
<a class="idref" href="coqrel.RelDefinitions.html#Monotonic"><span class="id" title="abbreviation">Monotonic</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#implb"><span class="id" title="definition">implb</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <a class="idref" href="coqrel.RelDefinitions.html#28fb2fb3952fac7e01eb907871e1ea99"><span class="id" title="notation">--></span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a> <a class="idref" href="coqrel.RelDefinitions.html#d5d0ad6beccd25d5224442d64ed307d5"><span class="id" title="notation">++></span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Bool.Bool.html#leb"><span class="id" title="definition">leb</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#implb"><span class="id" title="definition">implb</span></a>.<br/>
<span class="id" title="var">rauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
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