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liblayers.compcertx.InitMemMakeProgram.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link href="coqdoc.css" rel="stylesheet" type="text/css" />
<title>liblayers.compcertx.InitMemMakeProgram</title>
</head>
<body>
<div id="page">
<div id="header">
</div>
<div id="main">
<h1 class="libtitle">Library liblayers.compcertx.InitMemMakeProgram</h1>
<div class="code">
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Export</span> <a class="idref" href="liblayers.compcertx.MakeProgramFacts.html#"><span class="id" title="library">MakeProgramFacts</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Export</span> <a class="idref" href="liblayers.simrel.SimulationRelation.html#"><span class="id" title="library">SimulationRelation</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab584"></a><h1 class="section">Prerequisites</h1>
<div class="paragraph"> </div>
Some extra definitions and lemmas related to <span class="inlinecode"><a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#make_program"><span class="id" title="projection">make_program</span></a></span>.
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Section</span> <a name="MODULE_LAYER_ACCESS"><span class="id" title="section">MODULE_LAYER_ACCESS</span></a>.<br/>
<span class="id" title="keyword">Context</span> `{<span class="id" title="var">Hpf</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#ProgramFormat"><span class="id" title="class">ProgramFormat</span></a>}.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="get_module_layer_function_ok_none"><span class="id" title="lemma">get_module_layer_function_ok_none</span></a> {<span class="id" title="var">D</span>} <span class="id" title="var">i</span> (<span class="id" title="var">ML</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.module"><span class="id" title="variable">module</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D"><span class="id" title="variable">D</span></a>):<br/>
<a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">↔</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.logic.Modules.html#get_module_function"><span class="id" title="method">get_module_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</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="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.logic.Layers.html#get_layer_primitive"><span class="id" title="method">get_layer_primitive</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#snd"><span class="id" title="definition">snd</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>))<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a>.<br/>
<span class="id" title="tactic">split</span>.<br/>
+ <span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.logic.Modules.html#get_module_function"><span class="id" title="method">get_module_function</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>) <span class="id" title="keyword">as</span> [ [ | ] | ] ;<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.logic.Layers.html#get_layer_primitive"><span class="id" title="method">get_layer_primitive</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>) <span class="id" title="keyword">as</span> [ [ | ] | ] ;<br/>
<span class="id" title="tactic">simpl</span>;<br/>
<span class="id" title="tactic">clear</span>;<br/>
<span class="id" title="tactic">intuition</span> <span class="id" title="tactic">congruence</span>.<br/>
+ <span class="id" title="tactic">destruct</span> 1 <span class="id" title="keyword">as</span> (<span class="id" title="var">HM</span> & <span class="id" title="var">HL</span>).<br/>
<span class="id" title="tactic">rewrite</span> <span class="id" title="var">HM</span>.<br/>
<span class="id" title="tactic">rewrite</span> <span class="id" title="var">HL</span>.<br/>
<span class="id" title="tactic">reflexivity</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="get_module_layer_function_dec_aux"><span class="id" title="lemma">get_module_layer_function_dec_aux</span></a><br/>
{<span class="id" title="var">D</span>} (<span class="id" title="var">P</span>: <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Prop</span>) <span class="id" title="var">ML</span>:<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">(</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><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.logic.Modules.html#get_module_function"><span class="id" title="method">get_module_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</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="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.logic.Layers.html#get_layer_primitive"><span class="id" title="method">get_layer_primitive</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#snd"><span class="id" title="definition">snd</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</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="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">↔</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> (<span class="id" title="var">D</span> := <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">split</span>.<br/>
+ <span class="id" title="tactic">destruct</span> 1 <span class="id" title="keyword">as</span> (<span class="id" title="var">HM</span> & <span class="id" title="var">HL</span>).<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">HM</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">HL</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">HM</span> <span class="id" title="var">HL</span>.<br/>
<span class="id" title="tactic">repeat</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
|- <span class="id" title="keyword">context</span> [ ?<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> ] ⇒<br/>
<span class="id" title="tactic">replace</span> (<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="var">u</span>)<br/>
<span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_function_ok_none"><span class="id" title="lemma">get_module_layer_function_ok_none</span></a>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">tauto</span>.<br/>
+ <span class="id" title="tactic">intro</span> <span class="id" title="var">HML</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>;<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">HML</span> <span class="id" title="var">i</span>);<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">HML</span>;<br/>
(<span class="id" title="tactic">repeat</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
|- <span class="id" title="keyword">context</span> [ ?<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> ] ⇒<br/>
<span class="id" title="tactic">replace</span> (<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="var">u</span>)<br/>
<span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span><br/>
<span class="id" title="keyword">end</span>);<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_function_ok_none"><span class="id" title="lemma">get_module_layer_function_ok_none</span></a>;<br/>
<span class="id" title="tactic">clear</span>;<br/>
<span class="id" title="tactic">tauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="get_module_layer_function_dec"><span class="id" title="instance">get_module_layer_function_dec</span></a><br/>
`{<span class="id" title="var">Hmodules</span>: !<a class="idref" href="liblayers.logic.Modules.html#Modules"><span class="id" title="class">Modules</span></a> <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.Fm"><span class="id" title="variable">Fm</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.Vm"><span class="id" title="variable">Vm</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.module"><span class="id" title="variable">module</span></a>}<br/>
`{<span class="id" title="var">Hlayers</span>: !<a class="idref" href="liblayers.logic.Layers.html#Layers"><span class="id" title="class">Layers</span></a> <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.primsem"><span class="id" title="variable">primsem</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.Vm"><span class="id" title="variable">Vm</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.layer"><span class="id" title="variable">layer</span></a>}<br/>
{<span class="id" title="var">D</span>} (<span class="id" title="var">P</span>: <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Prop</span>):<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.lib.Decision.html#Decision"><span class="id" title="class">Decision.Decision</span></a> (<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">ML</span>,<br/>
<a class="idref" href="liblayers.lib.Decision.html#Decision"><span class="id" title="class">Decision.Decision</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> (<span class="id" title="var">D</span> := <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">X</span> <span class="id" title="var">ML</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="liblayers.lib.Decision.html#decide_rewrite"><span class="id" title="instance">Decision.decide_rewrite</span></a>.<br/>
{ <span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_function_dec_aux"><span class="id" title="lemma">get_module_layer_function_dec_aux</span></a>. }<br/>
<span class="id" title="var">typeclasses</span> <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Defined</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a> {<span class="id" title="var">D</span>} <span class="id" title="var">i</span> (<span class="id" title="var">ML</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.module"><span class="id" title="variable">module</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D"><span class="id" title="variable">D</span></a>):<br/>
<a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">↔</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.logic.Modules.html#get_module_variable"><span class="id" title="method">get_module_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</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="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.logic.Layers.html#get_layer_globalvar"><span class="id" title="method">get_layer_globalvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#snd"><span class="id" title="definition">snd</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>))<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a>.<br/>
<span class="id" title="tactic">split</span>.<br/>
+ <span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.logic.Modules.html#get_module_variable"><span class="id" title="method">get_module_variable</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>) <span class="id" title="keyword">as</span> [ [ <span class="id" title="var">gm</span> | ] | ] ;<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.logic.Layers.html#get_layer_globalvar"><span class="id" title="method">get_layer_globalvar</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>) <span class="id" title="keyword">as</span> [ [ <span class="id" title="var">gl</span> | ] | ] ;<br/>
<span class="id" title="tactic">simpl</span>;<br/>
<span class="id" title="tactic">clear</span>;<br/>
<span class="id" title="var">GlobalVars.res_option_globalvar_red</span>;<br/>
<span class="id" title="tactic">try</span> <span class="id" title="tactic">intuition</span> <span class="id" title="tactic">congruence</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.lib.Decision.html#decide"><span class="id" title="definition">Decision.decide</span></a> (<span class="id" title="var">gm</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="var">gl</span>)).<br/>
- <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">GlobalVars.res_option_globalvar_red</span>.<br/>
<span class="id" title="tactic">intuition</span> <span class="id" title="tactic">congruence</span>.<br/>
- <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.logic.GlobalVars.html#res_option_globalvar_oplus_diff"><span class="id" title="lemma">GlobalVars.res_option_globalvar_oplus_diff</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">assumption</span>.<br/>
<span class="id" title="tactic">intuition</span> <span class="id" title="tactic">congruence</span>.<br/>
+ <span class="id" title="tactic">destruct</span> 1 <span class="id" title="keyword">as</span> (<span class="id" title="var">HM</span> & <span class="id" title="var">HL</span>).<br/>
<span class="id" title="tactic">rewrite</span> <span class="id" title="var">HM</span>.<br/>
<span class="id" title="tactic">rewrite</span> <span class="id" title="var">HL</span>.<br/>
<span class="id" title="tactic">reflexivity</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="get_module_layer_variable_dec_aux"><span class="id" title="lemma">get_module_layer_variable_dec_aux</span></a><br/>
{<span class="id" title="var">D</span>} (<span class="id" title="var">P</span>: <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Prop</span>) <span class="id" title="var">ML</span>:<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">(</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><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.logic.Modules.html#get_module_variable"><span class="id" title="method">get_module_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</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="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.logic.Layers.html#get_layer_globalvar"><span class="id" title="method">get_layer_globalvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#snd"><span class="id" title="definition">snd</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</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="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">↔</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> (<span class="id" title="var">D</span> := <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">split</span>.<br/>
+ <span class="id" title="tactic">destruct</span> 1 <span class="id" title="keyword">as</span> (<span class="id" title="var">HM</span> & <span class="id" title="var">HL</span>).<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">HM</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">HL</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">HM</span> <span class="id" title="var">HL</span>.<br/>
<span class="id" title="tactic">repeat</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
|- <span class="id" title="keyword">context</span> [ ?<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> ] ⇒<br/>
<span class="id" title="tactic">replace</span> (<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="var">u</span>)<br/>
<span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">tauto</span>.<br/>
+ <span class="id" title="tactic">intro</span> <span class="id" title="var">HML</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>;<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">HML</span> <span class="id" title="var">i</span>);<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">HML</span>;<br/>
(<span class="id" title="tactic">repeat</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
|- <span class="id" title="keyword">context</span> [ ?<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> ] ⇒<br/>
<span class="id" title="tactic">replace</span> (<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="var">u</span>)<br/>
<span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span><br/>
<span class="id" title="keyword">end</span>);<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a>;<br/>
<span class="id" title="tactic">clear</span>;<br/>
<span class="id" title="tactic">tauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="get_module_layer_variable_dec"><span class="id" title="instance">get_module_layer_variable_dec</span></a><br/>
`{<span class="id" title="var">Hmodules</span>: !<a class="idref" href="liblayers.logic.Modules.html#Modules"><span class="id" title="class">Modules</span></a> <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.Fm"><span class="id" title="variable">Fm</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.Vm"><span class="id" title="variable">Vm</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.module"><span class="id" title="variable">module</span></a>}<br/>
`{<span class="id" title="var">Hlayers</span>: !<a class="idref" href="liblayers.logic.Layers.html#Layers"><span class="id" title="class">Layers</span></a> <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.primsem"><span class="id" title="variable">primsem</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.Vm"><span class="id" title="variable">Vm</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS.layer"><span class="id" title="variable">layer</span></a>}<br/>
{<span class="id" title="var">D</span>} (<span class="id" title="var">P</span>: <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Prop</span>):<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.lib.Decision.html#Decision"><span class="id" title="class">Decision.Decision</span></a> (<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">ML</span>,<br/>
<a class="idref" href="liblayers.lib.Decision.html#Decision"><span class="id" title="class">Decision.Decision</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> (<span class="id" title="var">D</span> := <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML"><span class="id" title="variable">ML</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">X</span> <span class="id" title="var">ML</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="liblayers.lib.Decision.html#decide_rewrite"><span class="id" title="instance">Decision.decide_rewrite</span></a>.<br/>
{ <span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_dec_aux"><span class="id" title="lemma">get_module_layer_variable_dec_aux</span></a>. }<br/>
<span class="id" title="var">typeclasses</span> <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Defined</span>.<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#MODULE_LAYER_ACCESS"><span class="id" title="section">MODULE_LAYER_ACCESS</span></a>.<br/>
<br/>
<span class="id" title="keyword">Section</span> <a name="RELATIONS"><span class="id" title="section">RELATIONS</span></a>.<br/>
<span class="id" title="keyword">Context</span> {<span class="id" title="var">ld1</span> <span class="id" title="var">Fm1</span> <span class="id" title="var">Vm1</span> <span class="id" title="var">Fp1</span> <span class="id" title="var">Vp1</span> <span class="id" title="var">module1</span> <span class="id" title="var">primsem1</span> <span class="id" title="var">layer1</span>}<br/>
`{<span class="id" title="var">pf_ops1</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#ProgramFormatOps"><span class="id" title="class">ProgramFormatOps</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ld1"><span class="id" title="variable">ld1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Fm1"><span class="id" title="variable">Fm1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Vm1"><span class="id" title="variable">Vm1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Fp1"><span class="id" title="variable">Fp1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Vp1"><span class="id" title="variable">Vp1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module1"><span class="id" title="variable">module1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#primsem1"><span class="id" title="variable">primsem1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#layer1"><span class="id" title="variable">layer1</span></a>}.<br/>
<span class="id" title="keyword">Context</span> {<span class="id" title="var">ld2</span> <span class="id" title="var">Fm2</span> <span class="id" title="var">Vm2</span> <span class="id" title="var">Fp2</span> <span class="id" title="var">Vp2</span> <span class="id" title="var">module2</span> <span class="id" title="var">primsem2</span> <span class="id" title="var">layer2</span>}<br/>
`{<span class="id" title="var">pf_ops2</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#ProgramFormatOps"><span class="id" title="class">ProgramFormatOps</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ld2"><span class="id" title="variable">ld2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Fm2"><span class="id" title="variable">Fm2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Vm2"><span class="id" title="variable">Vm2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Fp2"><span class="id" title="variable">Fp2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Vp2"><span class="id" title="variable">Vp2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module2"><span class="id" title="variable">module2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#primsem2"><span class="id" title="variable">primsem2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#layer2"><span class="id" title="variable">layer2</span></a>}.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="option_relation_forward_function_strong"><span class="id" title="lemma">option_relation_forward_function_strong</span></a> <span class="id" title="var">D1</span> <span class="id" title="var">D2</span> (<span class="id" title="var">RF</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#funrel"><span class="id" title="definition">funrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>) <span class="id" title="var">ML1</span> <span class="id" title="var">ML2</span>:<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a> (<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">f1</span> <span class="id" title="var">f2</span> ⇒<br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f1"><span class="id" title="variable">f1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f2"><span class="id" title="variable">f2</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f1"><span class="id" title="variable">f1</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f2"><span class="id" title="variable">f2</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">H</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">H</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">firstorder</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="option_relation_forward_variable_strong"><span class="id" title="lemma">option_relation_forward_variable_strong</span></a> <span class="id" title="var">D1</span> <span class="id" title="var">D2</span> (<span class="id" title="var">RV</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#varrel"><span class="id" title="definition">varrel</span></a>) (<span class="id" title="var">ML1</span>: <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <span class="id" title="var">_</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a>) (<span class="id" title="var">ML2</span>: <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <span class="id" title="var">_</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>):<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a> (<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RV"><span class="id" title="variable">RV</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">f1</span> <span class="id" title="var">f2</span> ⇒<br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RV"><span class="id" title="variable">RV</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f1"><span class="id" title="variable">f1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f2"><span class="id" title="variable">f2</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f1"><span class="id" title="variable">f1</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f2"><span class="id" title="variable">f2</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">H</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">H</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">firstorder</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="module_layer_rel_strong"><span class="id" title="definition">module_layer_rel_strong</span></a> (<span class="id" title="var">D1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.ld1"><span class="id" title="variable">ld1</span></a>) (<span class="id" title="var">D2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.ld2"><span class="id" title="variable">ld2</span></a>)<br/>
(<span class="id" title="var">RF</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#funrel"><span class="id" title="definition">funrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>) (<span class="id" title="var">RV</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#varrel"><span class="id" title="definition">varrel</span></a> (<span class="id" title="var">Vm1</span>:=<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.Vm1"><span class="id" title="variable">Vm1</span></a>) (<span class="id" title="var">Vm2</span>:=<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.Vm2"><span class="id" title="variable">Vm2</span></a>))<br/>
(<span class="id" title="var">ML1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.module1"><span class="id" title="variable">module1</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.layer1"><span class="id" title="variable">layer1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a>) (<span class="id" title="var">ML2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.module2"><span class="id" title="variable">module2</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.layer2"><span class="id" title="variable">layer2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>):<br/>
<span class="id" title="keyword">Prop</span> :=<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#module_layer_rel"><span class="id" title="definition">module_layer_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a><br/>
(<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> <span class="id" title="var">f1</span> <span class="id" title="var">f2</span> ⇒<br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f1"><span class="id" title="variable">f1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f2"><span class="id" title="variable">f2</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f1"><span class="id" title="variable">f1</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#f2"><span class="id" title="variable">f2</span></a>)<br/>
(<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> <span class="id" title="var">v1</span> <span class="id" title="var">v2</span> ⇒<br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RV"><span class="id" title="variable">RV</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#v1"><span class="id" title="variable">v1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#v2"><span class="id" title="variable">v2</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#v1"><span class="id" title="variable">v1</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</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="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#v2"><span class="id" title="variable">v2</span></a>)<br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="module_layer_rel_strengthen"><span class="id" title="lemma">module_layer_rel_strengthen</span></a> (<span class="id" title="var">D1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.ld1"><span class="id" title="variable">ld1</span></a>) (<span class="id" title="var">D2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.ld2"><span class="id" title="variable">ld2</span></a>)<br/>
(<span class="id" title="var">RF</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#funrel"><span class="id" title="definition">funrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>) (<span class="id" title="var">RV</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#varrel"><span class="id" title="definition">varrel</span></a> (<span class="id" title="var">Vm1</span>:=<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.Vm1"><span class="id" title="variable">Vm1</span></a>) (<span class="id" title="var">Vm2</span>:=<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.Vm2"><span class="id" title="variable">Vm2</span></a>))<br/>
(<span class="id" title="var">ML1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.module1"><span class="id" title="variable">module1</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.layer1"><span class="id" title="variable">layer1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a>) (<span class="id" title="var">ML2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.module2"><span class="id" title="variable">module2</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.layer2"><span class="id" title="variable">layer2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>):<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#module_layer_rel"><span class="id" title="definition">module_layer_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RV"><span class="id" title="variable">RV</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_rel_strong"><span class="id" title="definition">module_layer_rel_strong</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RV"><span class="id" title="variable">RV</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">H</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">HF</span> & <span class="id" title="var">HV</span>).<br/>
<span class="id" title="tactic">split</span>.<br/>
+ <span class="id" title="tactic">inversion</span> <span class="id" title="var">HF</span>; <span class="id" title="tactic">subst</span>; <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">auto</span>.<br/>
+ <span class="id" title="tactic">inversion</span> <span class="id" title="var">HV</span>; <span class="id" title="tactic">subst</span>; <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="module_layer_rel_weaken"><span class="id" title="lemma">module_layer_rel_weaken</span></a> (<span class="id" title="var">D1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.ld1"><span class="id" title="variable">ld1</span></a>) (<span class="id" title="var">D2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.ld2"><span class="id" title="variable">ld2</span></a>)<br/>
(<span class="id" title="var">RF</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#funrel"><span class="id" title="definition">funrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>) (<span class="id" title="var">RV</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#varrel"><span class="id" title="definition">varrel</span></a> (<span class="id" title="var">Vm1</span>:=<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.Vm1"><span class="id" title="variable">Vm1</span></a>) (<span class="id" title="var">Vm2</span>:=<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.Vm2"><span class="id" title="variable">Vm2</span></a>))<br/>
(<span class="id" title="var">ML1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.module1"><span class="id" title="variable">module1</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.layer1"><span class="id" title="variable">layer1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a>) (<span class="id" title="var">ML2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.module2"><span class="id" title="variable">module2</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS.layer2"><span class="id" title="variable">layer2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>):<br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_rel_strong"><span class="id" title="definition">module_layer_rel_strong</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RV"><span class="id" title="variable">RV</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#module_layer_rel"><span class="id" title="definition">module_layer_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RV"><span class="id" title="variable">RV</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">H</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">HF</span> & <span class="id" title="var">HV</span>).<br/>
<span class="id" title="tactic">split</span>.<br/>
+ <span class="id" title="tactic">inversion</span> <span class="id" title="var">HF</span>; <span class="id" title="tactic">subst</span>; <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">tauto</span>.<br/>
+ <span class="id" title="tactic">inversion</span> <span class="id" title="var">HV</span>; <span class="id" title="tactic">subst</span>; <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">tauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RELATIONS"><span class="id" title="section">RELATIONS</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab585"></a><h1 class="section">Proving <span class="inlinecode"><a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_program_rel"><span class="id" title="definition">simrel_program_rel</span></a></span></h1>
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Section</span> <a name="SIMREL_INIT_MEM"><span class="id" title="section">SIMREL_INIT_MEM</span></a>.<br/>
<span class="id" title="keyword">Context</span> `{<span class="id" title="var">Hmwd</span>: <a class="idref" href="liblayers.simrel.MemWithData.html#BaseMemoryModel"><span class="id" title="class">BaseMemoryModel</span></a>}.<br/>
<br/>
<span class="id" title="keyword">Context</span> {<span class="id" title="var">primsem</span> <span class="id" title="var">V</span> <span class="id" title="var">layer</span>} `{<span class="id" title="var">Hlayers</span>: <a class="idref" href="liblayers.logic.Layers.html#Layers"><span class="id" title="class">Layers</span></a> <a class="idref" href="liblayers.simrel.AbstractData.html#layerdata"><span class="id" title="record">layerdata</span></a> <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel"><span class="id" title="record">simrel</span></a> <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#primsem"><span class="id" title="variable">primsem</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#V"><span class="id" title="variable">V</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#layer"><span class="id" title="variable">layer</span></a>}<br/>
{<span class="id" title="var">module</span> <span class="id" title="var">F</span>} `{<span class="id" title="var">Hmodule_ops</span>: !<a class="idref" href="liblayers.logic.Modules.html#ModuleOps"><span class="id" title="class">ModuleOps</span></a> <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#V"><span class="id" title="variable">V</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module"><span class="id" title="variable">module</span></a>}<br/>
`{<span class="id" title="var">Hmodules</span>: !<a class="idref" href="liblayers.logic.Modules.html#Modules"><span class="id" title="class">Modules</span></a> <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#V"><span class="id" title="variable">V</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module"><span class="id" title="variable">module</span></a>}<br/>
`{<span class="id" title="var">Hmp</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#MakeProgram"><span class="id" title="class">MakeProgram</span></a>}.<br/>
<br/>
<span class="id" title="keyword">Context</span><br/>
{<span class="id" title="var">Fp</span> <span class="id" title="var">Vp</span>}<br/>
{<span class="id" title="var">pf</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#ProgramFormatOps"><span class="id" title="class">ProgramFormatOps</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.F"><span class="id" title="variable">F</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.V"><span class="id" title="variable">V</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Fp"><span class="id" title="variable">Fp</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Vp"><span class="id" title="variable">Vp</span></a>}<br/>
{<span class="id" title="var">Hpf</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#ProgramFormat"><span class="id" title="class">ProgramFormat</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.F"><span class="id" title="variable">F</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.V"><span class="id" title="variable">V</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Fp"><span class="id" title="variable">Fp</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Vp"><span class="id" title="variable">Vp</span></a>}<br/>
{<span class="id" title="var">Vp_eq_dec</span>: <a class="idref" href="liblayers.lib.Decision.html#EqDec"><span class="id" title="class">EqDec</span></a> (<a class="idref" href="compcert.common.AST.html#globvar"><span class="id" title="record">globvar</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#Vp"><span class="id" title="variable">Vp</span></a>)}.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a> {<span class="id" title="var">D1</span> <span class="id" title="var">D2</span>}<br/>
(<span class="id" title="var">R</span>: <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel"><span class="id" title="record">simrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>)<br/>
(<span class="id" title="var">ML1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.module"><span class="id" title="variable">module</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a>)<br/>
(<span class="id" title="var">ML2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.module"><span class="id" title="variable">module</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>) :=<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#7a45dffb109c3069e5c675be68643e60"><span class="id" title="notation">∨</span></a><br/>
<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_undef_matches_values_bool"><span class="id" title="projection">simrel_undef_matches_values_bool</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</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/>
<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="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<span class="id" title="keyword">match</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <span class="id" title="keyword">with</span><br/>
| <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <span class="id" title="var">v2</span>) ⇒<br/>
<span class="id" title="keyword">match</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#make_varinfo"><span class="id" title="method">make_varinfo</span></a> <span class="id" title="var">v2</span> <span class="id" title="keyword">with</span><br/>
| <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <span class="id" title="var">vp2</span> ⇒<br/>
<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_newvar_ok"><span class="id" title="definition">simrel_newvar_ok</span></a> (<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_new_glbl"><span class="id" title="projection">simrel_new_glbl</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a>) (<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_undef_matches_values_bool"><span class="id" title="projection">simrel_undef_matches_values_bool</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="compcert.common.AST.html#gvar_init"><span class="id" title="projection">gvar_init</span></a> <span class="id" title="var">vp2</span>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMem.html#Genv.init_data_list_valid"><span class="id" title="definition">Genv.init_data_list_valid</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#find_symbol"><span class="id" title="definition">find_symbol</span></a> 0 (<a class="idref" href="compcert.common.AST.html#gvar_init"><span class="id" title="projection">gvar_init</span></a> <span class="id" title="var">vp2</span>) <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="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a><br/>
<a class="idref" href="compcert.common.AST.html#gvar_readonly"><span class="id" title="projection">gvar_readonly</span></a> <span class="id" title="var">vp2</span> <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#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><br/>
<a class="idref" href="compcert.common.AST.html#gvar_volatile"><span class="id" title="projection">gvar_volatile</span></a> <span class="id" title="var">vp2</span> <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#false"><span class="id" title="constructor">false</span></a><br/>
| <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#False"><span class="id" title="inductive">False</span></a><br/>
<span class="id" title="keyword">end</span><br/>
| <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#False"><span class="id" title="inductive">False</span></a><br/>
<span class="id" title="keyword">end</span><br/>
<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="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#In"><span class="id" title="definition">List.In</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#map"><span class="id" title="definition">List.map</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> (<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_new_glbl"><span class="id" title="projection">simrel_new_glbl</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</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><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#Forall"><span class="id" title="inductive">Forall</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a>)) (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#map"><span class="id" title="definition">List.map</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> (<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_new_glbl"><span class="id" title="projection">simrel_new_glbl</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a>)).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="module_layer_init_rel_ext"><span class="id" title="lemma">module_layer_init_rel_ext</span></a> {<span class="id" title="var">D1</span> <span class="id" title="var">D2</span>} (<span class="id" title="var">R</span> <span class="id" title="var">R'</span>: <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel"><span class="id" title="record">simrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>)<br/>
(<span class="id" title="var">ML1</span> <span class="id" title="var">ML1'</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.module"><span class="id" title="variable">module</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a>)<br/>
(<span class="id" title="var">ML2</span> <span class="id" title="var">ML2'</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.module"><span class="id" title="variable">module</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>):<br/>
<a class="idref" href="liblayers.simrel.SimrelEquivalence.html#simrel_equiv"><span class="id" title="definition">SimrelEquivalence.simrel_equiv</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R'"><span class="id" title="variable">R'</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1'"><span class="id" title="variable">ML1'</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1'"><span class="id" title="variable">ML1'</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_function"><span class="id" title="definition">get_module_layer_function</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2'"><span class="id" title="variable">ML2'</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>,<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</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><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2'"><span class="id" title="variable">ML2'</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R'"><span class="id" title="variable">R'</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1'"><span class="id" title="variable">ML1'</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2'"><span class="id" title="variable">ML2'</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">Hequiv</span> <span class="id" title="var">Hfun1</span> <span class="id" title="var">Hvar1</span> <span class="id" title="var">Hfun2</span> <span class="id" title="var">Hvar2</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">Hfuns</span> & <span class="id" title="var">Hvars</span> & <span class="id" title="var">Hnew1</span> & <span class="id" title="var">Hnew2</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hequiv</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">equiv</span> & <span class="id" title="var">Hequiv</span>).<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">rewrite</span> <- <span class="id" title="var">Hfun2</span>.<br/>
<span class="id" title="tactic">rewrite</span> <- <span class="id" title="var">Hfun1</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hfuns</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hfuns</span>.<br/>
<span class="id" title="var">SimrelEquivalence.simrel_equiv_rewrite</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">rewrite</span> <- <span class="id" title="var">Hvar2</span>.<br/>
<span class="id" title="tactic">rewrite</span> <- <span class="id" title="var">Hvar1</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hvars</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hvars</span>.<br/>
<span class="id" title="var">SimrelEquivalence.simrel_equiv_rewrite</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">rewrite</span> <- <span class="id" title="var">Hvar1</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hnew1</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hnew1</span>.<br/>
<span class="id" title="var">SimrelEquivalence.simrel_equiv_rewrite</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
}<br/>
{<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#Forall_forall"><span class="id" title="lemma">Forall_forall</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Hnew2</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#Forall_forall"><span class="id" title="lemma">Forall_forall</span></a>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">rewrite</span> <- <span class="id" title="var">Hvar2</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hnew2</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hnew2</span>.<br/>
<span class="id" title="var">SimrelEquivalence.simrel_equiv_rewrite</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="module_layer_init_rel_dec"><span class="id" title="instance">module_layer_init_rel_dec</span></a> {<span class="id" title="var">D1</span> <span class="id" title="var">D2</span>} (<span class="id" title="var">R</span>: <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel"><span class="id" title="record">simrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>) <span class="id" title="var">ML1</span> <span class="id" title="var">ML2</span>:<br/>
<a class="idref" href="liblayers.lib.Decision.html#Decision"><span class="id" title="class">Decision</span></a> (<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">repeat</span> (<span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.lib.Decision.html#and_dec"><span class="id" title="instance">and_dec</span></a>; <span class="id" title="tactic">try</span> <span class="id" title="var">typeclasses</span> <span class="id" title="tactic">eauto</span>).<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_dec"><span class="id" title="instance">get_module_layer_variable_dec</span></a>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.lib.Decision.html#impl_dec"><span class="id" title="instance">impl_dec</span></a>; <span class="id" title="tactic">try</span> <span class="id" title="var">typeclasses</span> <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <span class="id" title="var">i</span> <span class="id" title="var">ML2</span>) <span class="id" title="keyword">as</span> [ [ <span class="id" title="var">g</span> | ] | ] ; <span class="id" title="tactic">try</span> <span class="id" title="var">now</span> (<span class="id" title="tactic">right</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#make_varinfo"><span class="id" title="method">make_varinfo</span></a> <span class="id" title="var">g</span>) <span class="id" title="keyword">as</span> [ | ] ; <span class="id" title="tactic">try</span> <span class="id" title="var">now</span> (<span class="id" title="tactic">right</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_newvar_ok"><span class="id" title="definition">simrel_newvar_ok</span></a>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.lib.Decision.html#and_dec"><span class="id" title="instance">and_dec</span></a>; <span class="id" title="tactic">try</span> <span class="id" title="var">typeclasses</span> <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Defined</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="get_module_layer_variable_context"><span class="id" title="lemma">get_module_layer_variable_context</span></a> {<span class="id" title="var">D</span>} <span class="id" title="var">i</span> <span class="id" title="var">CTXT</span> <span class="id" title="var">M</span> <span class="id" title="var">L</span>:<br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> (<span class="id" title="var">D</span> := <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#CTXT"><span class="id" title="variable">CTXT</span></a> <a class="idref" href="liblayers.logic.Structures.html#64a6660c5ed3e47856f7e7c848c9c807"><span class="id" title="notation">⊕</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#M"><span class="id" title="variable">M</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</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><br/>
<a class="idref" href="liblayers.logic.Modules.html#get_module_variable"><span class="id" title="method">get_module_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#CTXT"><span class="id" title="variable">CTXT</span></a> <a class="idref" href="liblayers.logic.Structures.html#64a6660c5ed3e47856f7e7c848c9c807"><span class="id" title="notation">⊕</span></a><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#M"><span class="id" title="variable">M</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#L"><span class="id" title="variable">L</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a>.<br/>
<span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.logic.Modules.html#get_module_variable_oplus"><span class="id" title="method">get_module_variable_oplus</span></a>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.logic.GlobalVars.html#res_option_globalvar_oplus_assoc"><span class="id" title="lemma">GlobalVars.res_option_globalvar_oplus_assoc</span></a>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="module_layer_init_rel_context"><span class="id" title="lemma">module_layer_init_rel_context</span></a> {<span class="id" title="var">D1</span> <span class="id" title="var">D2</span>}<br/>
(<span class="id" title="var">R</span>: <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel"><span class="id" title="record">simrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>)<br/>
(<span class="id" title="var">CTXT</span> <span class="id" title="var">M1</span> <span class="id" title="var">M2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.module"><span class="id" title="variable">module</span></a>)<br/>
(<span class="id" title="var">L1</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a>) (<span class="id" title="var">L2</span>: <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM.layer"><span class="id" title="variable">layer</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>):<br/>
<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.logic.Modules.html#get_module_variable"><span class="id" title="method">get_module_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#CTXT"><span class="id" title="variable">CTXT</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#get_module_layer_variable"><span class="id" title="definition">get_module_layer_variable</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#M2"><span class="id" title="variable">M2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#L2"><span class="id" title="variable">L2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#In"><span class="id" title="definition">List.In</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#map"><span class="id" title="definition">List.map</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> (<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_new_glbl"><span class="id" title="projection">simrel_new_glbl</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a>))<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#M1"><span class="id" title="variable">M1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#L1"><span class="id" title="variable">L1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#M2"><span class="id" title="variable">M2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#L2"><span class="id" title="variable">L2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#CTXT"><span class="id" title="variable">CTXT</span></a> <a class="idref" href="liblayers.logic.Structures.html#64a6660c5ed3e47856f7e7c848c9c807"><span class="id" title="notation">⊕</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#M1"><span class="id" title="variable">M1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#L1"><span class="id" title="variable">L1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#CTXT"><span class="id" title="variable">CTXT</span></a> <a class="idref" href="liblayers.logic.Structures.html#64a6660c5ed3e47856f7e7c848c9c807"><span class="id" title="notation">⊕</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#M2"><span class="id" title="variable">M2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#L2"><span class="id" title="variable">L2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">HCTXT</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a>.<br/>
<span class="id" title="tactic">destruct</span> 1 <span class="id" title="keyword">as</span> (<span class="id" title="var">Hfun</span> & <span class="id" title="var">Hvar2</span> & <span class="id" title="var">Hvar1</span> & <span class="id" title="var">Hnew</span>).<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">i</span> <span class="id" title="var">Hi</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hfun</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hi</span> <span class="id" title="var">Hfun</span>.<br/>
<span class="id" title="tactic">repeat</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
|- <span class="id" title="keyword">context</span> [ ?<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> ] ⇒<br/>
<span class="id" title="tactic">replace</span> (<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="var">u</span>)<br/>
<span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_function_ok_none"><span class="id" title="lemma">get_module_layer_function_ok_none</span></a>.<br/>
<span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.logic.Modules.html#get_module_function_none_oplus"><span class="id" title="lemma">get_module_function_none_oplus</span></a>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">tauto</span>.<br/>
}<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">i</span> <span class="id" title="var">Hi</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hvar2</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hi</span> <span class="id" title="var">Hvar2</span>.<br/>
<span class="id" title="tactic">repeat</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
|- <span class="id" title="keyword">context</span> [ ?<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> ] ⇒<br/>
<span class="id" title="tactic">replace</span> (<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="var">u</span>)<br/>
<span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">Hi</span> <span class="id" title="var">Hvar2</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a>.<br/>
<span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.logic.Modules.html#get_module_variable_none_oplus"><span class="id" title="lemma">get_module_variable_none_oplus</span></a>.<br/>
<span class="id" title="tactic">intros</span> [[<span class="id" title="var">CTXT_NONE</span> <span class="id" title="var">M1_NONE</span>] <span class="id" title="var">L1_NONE</span>].<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">CTXT_NONE</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_context"><span class="id" title="lemma">get_module_layer_variable_context</span></a>.<br/>
<span class="id" title="tactic">rewrite</span> <span class="id" title="var">CTXT_NONE</span>.<br/>
<span class="id" title="var">GlobalVars.res_option_globalvar_red</span>.<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">Hvar2</span>.<br/>
+ <span class="id" title="var">revert</span> <span class="id" title="var">Hi</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a>.<br/>
<span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.logic.Modules.html#get_module_variable_none_oplus"><span class="id" title="lemma">get_module_variable_none_oplus</span></a>.<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">CTXT_NONE</span>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">tauto</span>.<br/>
+ <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a>; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">i</span> <span class="id" title="var">Hi</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hvar1</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hi</span> <span class="id" title="var">Hvar1</span>.<br/>
<span class="id" title="tactic">repeat</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
|- <span class="id" title="keyword">context</span> [ ?<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a> ] ⇒<br/>
<span class="id" title="tactic">replace</span> (<span class="id" title="var">u</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="compcert.common.Errors.html#OK"><span class="id" title="constructor">OK</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isOKNone"><span class="id" title="definition">isOKNone</span></a> <span class="id" title="var">u</span>)<br/>
<span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">HCTXT</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">HCTXT</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#Forall_forall"><span class="id" title="lemma">Forall_forall</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Hnew</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hnew</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hnew</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a>.<br/>
<span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.logic.Modules.html#get_module_variable_none_oplus"><span class="id" title="lemma">get_module_variable_none_oplus</span></a>.<br/>
<span class="id" title="tactic">tauto</span>.<br/>
}<br/>
{<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hnew</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#Forall_forall"><span class="id" title="lemma">Forall_forall</span></a>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">Hnew</span>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hnew</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">Hnew</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#get_module_layer_variable_ok_none"><span class="id" title="lemma">get_module_layer_variable_ok_none</span></a>.<br/>
<span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">repeat</span> <span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.logic.Modules.html#get_module_variable_none_oplus"><span class="id" title="lemma">get_module_variable_none_oplus</span></a>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">tauto</span>.<br/>
}<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="simrel_not_new_glbl_spec"><span class="id" title="lemma">simrel_not_new_glbl_spec</span></a> <span class="id" title="var">ng</span> <span class="id" title="var">i</span>:<br/>
<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_not_new_glbl"><span class="id" title="definition">simrel_not_new_glbl</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ng"><span class="id" title="variable">ng</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#df1ced36fc33ce188051218bca314374"><span class="id" title="notation">↔</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#611abc97cba304de784fa909dbdea1fa"><span class="id" title="notation">¬</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#In"><span class="id" title="definition">In</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#map"><span class="id" title="definition">List.map</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ng"><span class="id" title="variable">ng</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#in_map_iff"><span class="id" title="lemma">in_map_iff</span></a>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_not_new_glbl"><span class="id" title="definition">simrel_not_new_glbl</span></a>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_new_glbl_for"><span class="id" title="definition">simrel_new_glbl_for</span></a>.<br/>
<span class="id" title="tactic">split</span>; <span class="id" title="tactic">intro</span> <span class="id" title="var">H</span>.<br/>
+ <span class="id" title="tactic">intro</span> <span class="id" title="var">ABS</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">ABS</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">x</span> & ? & <span class="id" title="var">Hx</span>).<br/>
<span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#in_split"><span class="id" title="lemma">in_split</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Hx</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hx</span> <span class="id" title="keyword">as</span> (? & ? & ?); <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.simrel.SimrelCategory.html#filter_app"><span class="id" title="lemma">SimrelCategory.filter_app</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.simrel.SimrelDefinition.html#test"><span class="id" title="definition">test</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.lib.Decision.html#decide"><span class="id" title="definition">decide</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> <span class="id" title="var">x</span> <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#fst"><span class="id" title="definition">fst</span></a> <span class="id" title="var">x</span>)); <span class="id" title="tactic">try</span> <span class="id" title="tactic">congruence</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="keyword">match</span> <span class="id" title="var">type</span> <span class="id" title="var">of</span> <span class="id" title="var">H</span> <span class="id" title="keyword">with</span><br/>
?<span class="id" title="var">e</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#5d35a99a6abff1d64bf70538feb70e36"><span class="id" title="notation">++</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="var">_</span> ⇒<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">e</span>; <span class="id" title="tactic">discriminate</span><br/>
<span class="id" title="keyword">end</span>.<br/>
+ <span class="id" title="var">revert</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">induction</span> <span class="id" title="var">ng</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.simrel.SimrelDefinition.html#test"><span class="id" title="definition">test</span></a> <span class="id" title="tactic">at</span> 1.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="liblayers.lib.Decision.html#decide"><span class="id" title="definition">decide</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#fst"><span class="id" title="definition">fst</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="var">i</span>)).<br/>
- <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">a</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="tactic">apply</span> <span class="id" title="var">IHng</span>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">ABSURD</span>.<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">ABSURD</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">x</span> & ? & <span class="id" title="var">Hx</span>).<br/>
<span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a name="simrel_program_rel_intro"><span class="id" title="lemma">simrel_program_rel_intro</span></a><br/>
{<span class="id" title="var">D1</span> <span class="id" title="var">D2</span>} (<span class="id" title="var">R</span>: <a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel"><span class="id" title="record">simrel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a>) <span class="id" title="var">ML1</span> <span class="id" title="var">ML2</span> <span class="id" title="var">RF</span>:<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span> : <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a>, <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a> (<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="coqrel.RelDefinitions.html#Monotonic"><span class="id" title="abbreviation">Monotonic</span></a> (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#make_fundef"><span class="id" title="definition">make_fundef</span></a> <span class="id" title="var">_</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="coqrel.RelOperators.html#22d5c754b43f74bbc26a31adf4b8647c"><span class="id" title="notation">@@</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</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.Program.Basics.html#impl"><span class="id" title="definition">impl</span></a> <a class="idref" href="coqrel.RelOperators.html#22d5c754b43f74bbc26a31adf4b8647c"><span class="id" title="notation">@@</span></a> <a class="idref" href="liblayers.compcertx.ErrorMonad.html#isError"><span class="id" title="definition">isError</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#module_layer_rel"><span class="id" title="definition">module_layer_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#RF"><span class="id" title="variable">RF</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="liblayers.logic.OptionOrders.html#option_le"><span class="id" title="inductive">option_le</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#eq"><span class="id" title="inductive">eq</span></a>) <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_init_rel"><span class="id" title="definition">module_layer_init_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.ErrorMonad.html#res_le"><span class="id" title="inductive">res_le</span></a> (<a class="idref" href="liblayers.simrel.SimrelDefinition.html#simrel_program_rel"><span class="id" title="definition">simrel_program_rel</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#R"><span class="id" title="variable">R</span></a>) (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#make_program"><span class="id" title="method">make_program</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML1"><span class="id" title="variable">ML1</span></a>) (<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#make_program"><span class="id" title="method">make_program</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#ML2"><span class="id" title="variable">ML2</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">HRF</span> <span class="id" title="var">HRFerr</span> <span class="id" title="var">Hrel</span> <span class="id" title="var">Hinit</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#module_layer_rel_strengthen"><span class="id" title="lemma">module_layer_rel_strengthen</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Hrel</span>.<br/>
<span class="id" title="tactic">red</span> <span class="id" title="keyword">in</span> <span class="id" title="var">Hrel</span>.<br/>
<span class="id" title="tactic">eapply</span> @<a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#make_program_rel"><span class="id" title="method">make_program_rel</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Hrel</span>.<br/>
2: <span class="id" title="var">eassumption</span>.<br/>
2: <span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#foodef_rel_mpr"><span class="id" title="instance">foodef_rel_mpr</span></a>.<br/>
2: <span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#option_relation_forward_function_strong"><span class="id" title="lemma">option_relation_forward_function_strong</span></a>; <span class="id" title="tactic">assumption</span>.<br/>
× <span class="id" title="tactic">inversion</span> <span class="id" title="var">Hrel</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hrel</span>; <span class="id" title="tactic">constructor</span>.<br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
<span class="id" title="var">K</span>: <a class="idref" href="liblayers.compcertx.CompcertStructures.html#program_rel"><span class="id" title="record">program_rel</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> ⇒<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">K</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#program_subrel"><span class="id" title="instance">program_subrel</span></a>.<br/>
+ <span class="id" title="tactic">intros</span> <span class="id" title="var">i</span> <span class="id" title="var">fp1</span> <span class="id" title="var">fp2</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#fundef_rel"><span class="id" title="definition">fundef_rel</span></a>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">Hf</span>.<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hf</span> <span class="id" title="keyword">as</span> [ <span class="id" title="var">f1</span> ? <span class="id" title="var">Hfp1</span> <span class="id" title="var">f2</span> ? <span class="id" title="var">Hfp2</span> <span class="id" title="var">Hf_</span> ]; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hf</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hf_</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">Hf</span> & <span class="id" title="var">HF1</span> & <span class="id" title="var">HF2</span>).<br/>
<span class="id" title="tactic">red</span>.<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hfp2</span>; <span class="id" title="tactic">subst</span>.<br/>
- <span class="id" title="tactic">inversion</span> <span class="id" title="var">Hfp1</span>; <span class="id" title="tactic">subst</span>; <span class="id" title="tactic">try</span> <span class="id" title="var">now</span> <span class="id" title="tactic">repeat</span> <span class="id" title="tactic">constructor</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hinit</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">Hfuns</span> & <span class="id" title="var">_</span>).<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hfuns</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hfuns</span>; <span class="id" title="tactic">try</span> <span class="id" title="tactic">congruence</span>.<br/>
<span class="id" title="tactic">constructor</span>.<br/>
<span class="id" title="tactic">assumption</span>.<br/>
- <span class="id" title="tactic">apply</span> <span class="id" title="var">HRF</span> <span class="id" title="keyword">in</span> <span class="id" title="var">Hf</span>.<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hf</span> (<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#eq_refl"><span class="id" title="constructor">eq_refl</span></a> <span class="id" title="var">_</span>)).<br/>
<span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hfp1</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">constructor</span>.<br/>
+ <span class="id" title="tactic">intros</span> <span class="id" title="var">i</span> <span class="id" title="var">vp1</span> <span class="id" title="var">vp2</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#vardef_rel"><span class="id" title="definition">vardef_rel</span></a>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">Hv</span>.<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hv</span> <span class="id" title="keyword">as</span> [ <span class="id" title="var">v1</span> ? <span class="id" title="var">Hvp1</span> <span class="id" title="var">v2</span> ? <span class="id" title="var">Hvp2</span> <span class="id" title="var">Hv_</span> ]; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hv</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hv_</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">Hv</span> & <span class="id" title="var">HV1</span> & <span class="id" title="var">HV2</span>).<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hvp2</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hvp2</span>; <span class="id" title="tactic">subst</span>.<br/>
- <span class="id" title="tactic">inversion</span> <span class="id" title="var">Hv</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hv</span>; <span class="id" title="tactic">subst</span>.<br/>
{<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hvp1</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hvp1</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hinit</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">_</span> & <span class="id" title="var">Hvar</span> & <span class="id" title="var">_</span>).<br/>
<span class="id" title="tactic">specialize</span> (<span class="id" title="var">Hvar</span> <span class="id" title="var">i</span>).<br/>
<span class="id" title="var">exploit</span> <span class="id" title="var">Hvar</span>.<br/>
{ <span class="id" title="tactic">congruence</span>. }<br/>
{ <span class="id" title="tactic">assumption</span>. }<br/>
<span class="id" title="tactic">rewrite</span> <span class="id" title="var">HV2</span>.<br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
<span class="id" title="var">K</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#match_vardef"><span class="id" title="definition">match_vardef</span></a> <span class="id" title="var">_</span> ?<span class="id" title="var">u</span> |- <span class="id" title="var">_</span> ⇒<br/>
<span class="id" title="tactic">rename</span> <span class="id" title="var">K</span> <span class="id" title="var">into</span> <span class="id" title="var">Hvardef</span>;<br/>
<span class="id" title="tactic">rename</span> <span class="id" title="var">u</span> <span class="id" title="var">into</span> <span class="id" title="var">vp</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#match_vardef"><span class="id" title="definition">match_vardef</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Hvardef</span>.<br/>
<span class="id" title="tactic">rewrite</span> <span class="id" title="var">Hvardef</span>.<br/>
<span class="id" title="tactic">destruct</span> 1 <span class="id" title="keyword">as</span> (<span class="id" title="var">Hvarok</span> & <span class="id" title="var">Hvalid</span> & <span class="id" title="var">Hreadonly</span> & <span class="id" title="var">Hvolatile</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">vp</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> ×.<br/>
<span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hvp1</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
<span class="id" title="var">K1</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#match_vardef"><span class="id" title="definition">match_vardef</span></a> <span class="id" title="var">_</span> ?<span class="id" title="var">u1</span>,<br/>
<span class="id" title="var">K2</span>: <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#match_vardef"><span class="id" title="definition">match_vardef</span></a> <span class="id" title="var">_</span> ?<span class="id" title="var">u2</span> |- <span class="id" title="var">_</span> ⇒<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#match_vardef"><span class="id" title="definition">match_vardef</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">K1</span>, <span class="id" title="var">K2</span>;<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">u2</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <span class="id" title="var">u1</span>) <span class="id" title="tactic">by</span> <span class="id" title="tactic">congruence</span>;<br/>
<span class="id" title="tactic">subst</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">constructor</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#simrel_not_new_glbl_spec"><span class="id" title="lemma">simrel_not_new_glbl_spec</span></a>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hinit</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">_</span> & <span class="id" title="var">_</span> & <span class="id" title="var">Hnew1</span> & <span class="id" title="var">_</span>).<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">Hnew1</span>.<br/>
<span class="id" title="tactic">congruence</span>.<br/>
- <span class="id" title="tactic">inversion</span> <span class="id" title="var">Hv</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hv</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hvp1</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">Hvp1</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">constructor</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#simrel_not_new_glbl_spec"><span class="id" title="lemma">simrel_not_new_glbl_spec</span></a>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">Hinit</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">_</span> & <span class="id" title="var">_</span> & <span class="id" title="var">_</span> & <span class="id" title="var">Hnew2</span>).<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">ABSURD</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#Forall_forall"><span class="id" title="lemma">Forall_forall</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Hnew2</span>.<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">Hnew2</span> <span class="id" title="keyword">in</span> <span class="id" title="var">ABSURD</span>.<br/>
<span class="id" title="var">contradiction</span>.<br/>
× <span class="id" title="tactic">intro</span> <span class="id" title="var">i</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.MakeProgramSpec.html#OptionRelationForward"><span class="id" title="class">OptionRelationForward</span></a>.<br/>
<span class="id" title="tactic">destruct</span> 1 <span class="id" title="keyword">as</span> (<span class="id" title="var">Hopt</span> & <span class="id" title="var">_</span>).<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hopt</span>; <span class="id" title="tactic">subst</span>; <span class="id" title="tactic">congruence</span>.<br/>
× <span class="id" title="tactic">intros</span> <span class="id" title="var">i</span> <span class="id" title="var">f1</span> <span class="id" title="var">f2</span> (<span class="id" title="var">Hf</span> & <span class="id" title="var">Hf1</span> & <span class="id" title="var">Hf2</span>).<br/>
<span class="id" title="tactic">try</span> <span class="id" title="var">rauto</span>. <span class="id" title="tactic">eapply</span> <span class="id" title="var">HRFerr</span>.<br/>
<span class="id" title="tactic">assumption</span>.<br/>
× <span class="id" title="tactic">intros</span> <span class="id" title="var">i</span> <span class="id" title="var">v1</span> <span class="id" title="var">v2</span> (<span class="id" title="var">Hv</span> & <span class="id" title="var">Hv1</span> & <span class="id" title="var">Hv2</span>).<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">Hv</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">reflexivity</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="liblayers.compcertx.InitMemMakeProgram.html#SIMREL_INIT_MEM"><span class="id" title="section">SIMREL_INIT_MEM</span></a>.<br/>
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