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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<html xmlns="http://www.w3.org/1999/xhtml">
<head>
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<title>liblayers.compcertx.CGenSem</title>
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<body>
<div id="page">
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<h1 class="libtitle">Library liblayers.compcertx.CGenSem</h1>
<div class="code">
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="liblayers.simrel.AbstractData.html#"><span class="id" title="library">AbstractData</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Export</span> <a class="idref" href="liblayers.compcertx.CPrimitives.html#"><span class="id" title="library">CPrimitives</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Export</span> <a class="idref" href="liblayers.compcertx.GenSem.html#"><span class="id" title="library">GenSem</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="liblayers.simrel.MemWithData.html#"><span class="id" title="library">MemWithData</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="liblayers.simrel.SimrelDefinition.html#"><span class="id" title="library">SimrelDefinition</span></a> <a class="idref" href="liblayers.compcertx.SimValues.html#"><span class="id" title="library">SimValues</span></a> <a class="idref" href="liblayers.simrel.SimrelLessdef.html#"><span class="id" title="library">SimrelLessdef</span></a> <a class="idref" href="liblayers.simrel.SimrelInject.html#"><span class="id" title="library">SimrelInject</span></a>.<br/>
<br/>
<span class="id" title="keyword">Section</span> <a name="WITHMEM"><span class="id" title="section">WITHMEM</span></a>.<br/>
<span class="id" title="keyword">Context</span> `{<span class="id" title="var">Hmem</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">Inductive</span> <a name="csemof"><span class="id" title="inductive">csemof</span></a> <br/>
(<span class="id" title="var">D</span>: <a class="idref" href="liblayers.simrel.AbstractData.html#layerdata"><span class="id" title="record">layerdata</span></a>) {<span class="id" title="var">T</span>: <span class="id" title="keyword">Type</span>}<br/>
{<span class="id" title="var">targs</span> <span class="id" title="var">tres</span>}<br/>
`{<span class="id" title="var">semof_ops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semof"><span class="id" title="class">GenSem.Semof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#targs"><span class="id" title="variable">targs</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#tres"><span class="id" title="variable">tres</span></a>}<br/>
(<span class="id" title="var">f</span>: <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>): <br/>
<a class="idref" href="liblayers.compcertx.CompcertStructures.html#csignature"><span class="id" title="record">csignature</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.Datatypes.html#list"><span class="id" title="inductive">list</span></a> <a class="idref" href="compcert.common.Values.html#val"><span class="id" title="inductive">val</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.simrel.MemWithData.html#mwd"><span class="id" title="definition">mwd</span></a> <span class="id" title="var">D</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> <a class="idref" href="compcert.common.Values.html#val"><span class="id" title="inductive">val</span></a> <a class="idref" href="liblayers.lib.Functor.html#3c95d747e965984bdabf05c6b0e23759"><span class="id" title="notation">×</span></a> <a class="idref" href="liblayers.simrel.MemWithData.html#mwd"><span class="id" title="definition">mwd</span></a> <span class="id" title="var">D</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 name="csemof_intro"><span class="id" title="constructor">csemof_intro</span></a> <span class="id" title="var">args</span> <span class="id" title="var">m</span> <span class="id" title="var">d</span> <span class="id" title="var">res</span> <span class="id" title="var">d'</span>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">csg</span>,<br/>
<a class="idref" href="liblayers.compcertx.CGenSem.html#csg"><span class="id" title="variable">csg</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.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">{|</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">csig_args</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">:=</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">targs</span></a><a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">;</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">csig_res</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">:=</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">tres</span></a><a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">;</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">csig_cc</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">:=</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">AST.cc_default</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.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="liblayers.compcertx.GenSem.html#semof"><span class="id" title="definition">semof</span></a> <span class="id" title="var">f</span> <a class="idref" href="liblayers.compcertx.CGenSem.html#args"><span class="id" title="variable">args</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#res"><span class="id" title="variable">res</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d'"><span class="id" title="variable">d'</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.CGenSem.html#csemof"><span class="id" title="inductive">csemof</span></a> <span class="id" title="var">D</span> <span class="id" title="var">f</span> <a class="idref" href="liblayers.compcertx.CGenSem.html#csg"><span class="id" title="variable">csg</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.CGenSem.html#args"><span class="id" title="variable">args</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.CGenSem.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.CGenSem.html#d"><span class="id" title="variable">d</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.CGenSem.html#res"><span class="id" title="variable">res</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.CGenSem.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.CGenSem.html#d'"><span class="id" title="variable">d'</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/>
<br/>
<span class="id" title="var">Program</span><br/>
<span class="id" title="keyword">Definition</span><br/>
<a name="cgensem"><span class="id" title="definition">cgensem</span></a><br/>
(<span class="id" title="var">D</span>: <a class="idref" href="liblayers.simrel.AbstractData.html#layerdata"><span class="id" title="record">layerdata</span></a>) {<span class="id" title="var">T</span>: <span class="id" title="keyword">Type</span>}<br/>
{<span class="id" title="var">targs</span> <span class="id" title="var">tres</span>}<br/>
`{<span class="id" title="var">semof_ops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semof"><span class="id" title="class">Semof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#targs"><span class="id" title="variable">targs</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#tres"><span class="id" title="variable">tres</span></a>}<br/>
{<span class="id" title="var">semprops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semprops"><span class="id" title="class">Semprops</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>}<br/>
(<span class="id" title="var">f</span>: <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>): <a class="idref" href="liblayers.compcertx.CPrimitives.html#cprimitive"><span class="id" title="record">cprimitive</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> :=<br/>
<a class="idref" href="liblayers.compcertx.CPrimitives.html#mkcprimitive"><span class="id" title="definition">mkcprimitive</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a><br/>
(<a class="idref" href="liblayers.compcertx.CGenSem.html#csemof"><span class="id" title="inductive">csemof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#f"><span class="id" title="variable">f</span></a>)<br/>
{| <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">csig_args</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">:=</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">targs</span></a><a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">;</span></a><br/>
<a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">csig_res</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">:=</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">tres</span></a><a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">;</span></a><br/>
<a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">csig_cc</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">:=</span></a> <a class="idref" href="liblayers.compcertx.CompcertStructures.html#Build_csignature"><span class="id" title="constructor">AST.cc_default</span></a> |}<br/>
<span class="id" title="var">_</span>.<br/>
<span class="id" title="keyword">Next</span> <span class="id" title="keyword">Obligation</span>.<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">H</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="liblayers.compcertx.GenSem.html#semprops_well_typed"><span class="id" title="method">semprops_well_typed</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="semprops_to_cprimitive_extcall_props"><span class="id" title="instance">semprops_to_cprimitive_extcall_props</span></a><br/>
{<span class="id" title="var">D</span>: <a class="idref" href="liblayers.simrel.AbstractData.html#layerdata"><span class="id" title="record">layerdata</span></a>} {<span class="id" title="var">T</span> <span class="id" title="var">targs</span> <span class="id" title="var">tres</span>} (<span class="id" title="var">f</span>: <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>):<br/>
<span class="id" title="keyword">∀</span> (<span class="id" title="var">semof_ops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semof"><span class="id" title="class">Semof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#targs"><span class="id" title="variable">targs</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#tres"><span class="id" title="variable">tres</span></a>)<br/>
(<span class="id" title="var">semprops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semprops"><span class="id" title="class">Semprops</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>),<br/>
<a class="idref" href="liblayers.compcertx.CPrimitives.html#CPrimitiveExtcallProperties"><span class="id" title="class">CPrimitiveExtcallProperties</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> (<a class="idref" href="liblayers.compcertx.CGenSem.html#cgensem"><span class="id" title="definition">cgensem</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#f"><span class="id" title="variable">f</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">semof</span> <span class="id" title="var">PROPS</span>.<br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">PROPS</span>.<br/>
<span class="id" title="tactic">constructor</span>.<br/>
+ <br/>
<span class="id" title="tactic">constructor</span>; [ | <span class="id" title="tactic">unfold</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#incl"><span class="id" title="definition">incl</span></a>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span> ].<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">p</span> <span class="id" title="var">sg</span> [<span class="id" title="var">args1</span> [<span class="id" title="var">m1</span> <span class="id" title="var">d1</span>]] [<span class="id" title="var">args2</span> [<span class="id" title="var">m2</span> <span class="id" title="var">d2</span>]] .<br/>
<span class="id" title="tactic">inversion</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.simrel.SimrelLessdef.html#match_strong_extends_val"><span class="id" title="lemma">match_strong_extends_val</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">assert</span> (<a class="idref" href="compcert.common.Values.html#Val.lessdef_list"><span class="id" title="inductive">Val.lessdef_list</span></a> <span class="id" title="var">args1</span> <span class="id" title="var">args2</span>) <span class="id" title="keyword">as</span> <span class="id" title="var">LESSDEF</span>.<br/>
{<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">induction</span> 1; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">intros</span> [<span class="id" title="var">res1</span> [<span class="id" title="var">m1'</span> <span class="id" title="var">d1'</span>]].<br/>
<span class="id" title="tactic">inversion</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">exploit</span> <span class="id" title="var">semprops_lessdef</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">intro</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H1</span>.<br/>
<span class="id" title="var">exploit</span> (<a class="idref" href="liblayers.simrel.SimrelLessdef.html#strong_extends_elim"><span class="id" title="lemma">strong_extends_elim</span></a> (<span class="id" title="var">D</span>:=<span class="id" title="var">D</span>)); <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="var">lift_simpl</span>.<br/>
<span class="id" title="tactic">destruct</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">esplit</span>.<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
}<br/>
<span class="id" title="tactic">assert</span> (<a class="idref" href="compcert.common.Memtype.html#Mem.extends"><span class="id" title="method">Mem.extends</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><span class="id" title="var">m1'</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <span class="id" title="var">d1'</span><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><span class="id" title="var">m2</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <span class="id" title="var">d1'</span><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/>
{<br/>
<span class="id" title="var">lift_simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="var">edestruct</span> (<a class="idref" href="liblayers.simrel.SimrelLessdef.html#strong_extends_le_intro"><span class="id" title="lemma">strong_extends_le_intro</span></a> (<span class="id" title="var">D</span> := <span class="id" title="var">D</span>)) <span class="id" title="keyword">as</span> [ ? [? ?]] ; <span class="id" title="tactic">eauto</span>.<br/>
{<br/>
<span class="id" title="var">lift_simpl</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.common.Memtype.html#Mem.unchanged_on_refl"><span class="id" title="lemma">Mem.unchanged_on_refl</span></a>.<br/>
}<br/>
{<br/>
<span class="id" title="var">lift_simpl</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.common.Memtype.html#Mem.unchanged_on_refl"><span class="id" title="lemma">Mem.unchanged_on_refl</span></a>.<br/>
} <br/>
<span class="id" title="var">esplit</span>.<br/>
<span class="id" title="tactic">split</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">simpl</span>.<br/>
{<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.simrel.SimrelLessdef.html#match_strong_extends_val"><span class="id" title="lemma">match_strong_extends_val</span></a>.<br/>
<span class="id" title="tactic">reflexivity</span>.<br/>
}<br/>
{<br/>
<span class="id" title="var">lift_simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<br/>
+ <br/>
<span class="id" title="tactic">constructor</span>; [ | <span class="id" title="tactic">unfold</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Lists.List.html#incl"><span class="id" title="definition">incl</span></a>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span> ].<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">p</span> <span class="id" title="var">sg</span> [<span class="id" title="var">args1</span> [<span class="id" title="var">m1</span> <span class="id" title="var">d1</span>]] [<span class="id" title="var">args2</span> [<span class="id" title="var">m2</span> <span class="id" title="var">d2</span>]] .<br/>
<span class="id" title="tactic">inversion</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.simrel.SimrelInject.html#match_val_strong_inject"><span class="id" title="lemma">match_val_strong_inject</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">assert</span> (<a class="idref" href="compcert.common.Values.html#Val.inject_list"><span class="id" title="inductive">Val.inject_list</span></a> (<a class="idref" href="liblayers.simrel.SimrelInject.html#simrel_inject_meminj"><span class="id" title="projection">simrel_inject_meminj</span></a> (<a class="idref" href="liblayers.simrel.SimrelInject.html#strong_inject_meminj"><span class="id" title="projection">strong_inject_meminj</span></a> <span class="id" title="var">p</span>)) <span class="id" title="var">args1</span> <span class="id" title="var">args2</span>) <span class="id" title="keyword">as</span> <span class="id" title="var">INJECT</span>.<br/>
{<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">clear</span>.<br/>
<span class="id" title="tactic">induction</span> 1; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">intros</span> [<span class="id" title="var">res1</span> [<span class="id" title="var">m1'</span> <span class="id" title="var">d1'</span>]].<br/>
<span class="id" title="tactic">inversion</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">exploit</span> <span class="id" title="var">semprops_inject</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">intro</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H1</span>.<br/>
<span class="id" title="var">exploit</span> (<a class="idref" href="liblayers.simrel.SimrelInject.html#strong_inject_elim'"><span class="id" title="lemma">strong_inject_elim'</span></a> (<span class="id" title="var">D</span> := <span class="id" title="var">D</span>)); <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">intro</span> <span class="id" title="var">INJ'</span>.<br/>
<span class="id" title="var">exploit</span> (<a class="idref" href="liblayers.simrel.SimrelInject.html#simrel_inject_match_mem_base"><span class="id" title="projection">simrel_inject_match_mem_base</span></a> (<span class="id" title="var">D</span> := <span class="id" title="var">D</span>)); <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="var">lift_simpl</span>.<br/>
<span class="id" title="tactic">destruct</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">esplit</span>.<br/>
<span class="id" title="tactic">split</span>.<br/>
{<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
}<br/>
<span class="id" title="tactic">assert</span> (<a class="idref" href="compcert.common.Memtype.html#Mem.inject"><span class="id" title="method">Mem.inject</span></a> (<a class="idref" href="liblayers.simrel.SimrelInject.html#simrel_inject_meminj"><span class="id" title="projection">simrel_inject_meminj</span></a> (<a class="idref" href="liblayers.simrel.SimrelInject.html#strong_inject_meminj"><span class="id" title="projection">strong_inject_meminj</span></a> <span class="id" title="var">p</span>)) <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><span class="id" title="var">m1'</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <span class="id" title="var">d1'</span><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><span class="id" title="var">m2</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <span class="id" title="var">d1'</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>) <span class="id" title="keyword">as</span> <span class="id" title="var">INJ_POST</span>.<br/>
{<br/>
<span class="id" title="var">lift_simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
} <br/>
<span class="id" title="var">edestruct</span> (<a class="idref" href="liblayers.simrel.SimrelInject.html#strong_inject_acc_intro"><span class="id" title="lemma">strong_inject_acc_intro</span></a> (<span class="id" title="var">D</span> := <span class="id" title="var">D</span>)) <span class="id" title="keyword">as</span> [ ? [? [? ?]]] ; <span class="id" title="tactic">eauto</span>.<br/>
{<br/>
<span class="id" title="tactic">red</span>. <span class="id" title="tactic">congruence</span>.<br/>
}<br/>
{<br/>
<span class="id" title="var">lift_simpl</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.common.Memtype.html#Mem.unchanged_on_refl"><span class="id" title="lemma">Mem.unchanged_on_refl</span></a>.<br/>
}<br/>
{<br/>
<span class="id" title="var">lift_simpl</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.common.Memtype.html#Mem.unchanged_on_refl"><span class="id" title="lemma">Mem.unchanged_on_refl</span></a>.<br/>
} <br/>
<span class="id" title="var">esplit</span>.<br/>
<span class="id" title="tactic">split</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">simpl</span>.<br/>
{<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="liblayers.simrel.SimrelInject.html#match_val_strong_inject"><span class="id" title="lemma">match_val_strong_inject</span></a>.<br/>
<span class="id" title="tactic">eauto</span>.<br/>
}<br/>
{<br/>
<span class="id" title="var">lift_simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<br/>
+ <br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">clear</span>. <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">intuition</span> <span class="id" title="tactic">congruence</span>.<br/>
<br/>
+ <br/>
<span class="id" title="tactic">inversion</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">inversion</span> 1; <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">U</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#semof"><span class="id" title="definition">GenSem.semof</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">V</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#semof"><span class="id" title="definition">GenSem.semof</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">_</span> ⇒<br/>
<span class="id" title="tactic">generalize</span> (<span class="id" title="var">semprops_determ</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">U</span> <span class="id" title="var">V</span>)<br/>
<span class="id" title="keyword">end</span>.<br/>
<span class="id" title="tactic">clear</span>. <span class="id" title="tactic">intuition</span> <span class="id" title="tactic">congruence</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Class</span> <a name="GenSemPreservesInvariant"><span class="id" title="record">GenSemPreservesInvariant</span></a><br/>
(<span class="id" title="var">D</span>: <a class="idref" href="liblayers.simrel.AbstractData.html#layerdata"><span class="id" title="record">layerdata</span></a>) {<span class="id" title="var">T</span>: <span class="id" title="keyword">Type</span>}<br/>
{<span class="id" title="var">targs</span> <span class="id" title="var">tres</span>}<br/>
`{<span class="id" title="var">semof_ops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semof"><span class="id" title="class">GenSem.Semof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#targs"><span class="id" title="variable">targs</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#tres"><span class="id" title="variable">tres</span></a>}<br/>
(<span class="id" title="var">f</span>: <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>)<br/>
:=<br/>
{<br/>
<a name="gensem_preserves_invariant_data_inv"><span class="id" title="projection">gensem_preserves_invariant_data_inv</span></a> <span class="id" title="var">args</span> <span class="id" title="var">d</span> <span class="id" title="var">res</span> <span class="id" title="var">d'</span> <span class="id" title="var">j</span>:<br/>
<a class="idref" href="liblayers.compcertx.GenSem.html#semof"><span class="id" title="definition">semof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#args"><span class="id" title="variable">args</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#res"><span class="id" title="variable">res</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d'"><span class="id" title="variable">d'</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.simrel.AbstractData.html#data_inject"><span class="id" title="method">data_inject</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</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.simrel.AbstractData.html#data_inv"><span class="id" title="method">data_inv</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</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.simrel.AbstractData.html#data_inv"><span class="id" title="method">data_inv</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d'"><span class="id" title="variable">d'</span></a>;<br/>
<a name="gensem_preserves_invariant_data_inject"><span class="id" title="projection">gensem_preserves_invariant_data_inject</span></a> <span class="id" title="var">args</span> <span class="id" title="var">d</span> <span class="id" title="var">res</span> <span class="id" title="var">d'</span> <span class="id" title="var">j</span>:<br/>
<a class="idref" href="liblayers.compcertx.GenSem.html#semof"><span class="id" title="definition">semof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#args"><span class="id" title="variable">args</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#res"><span class="id" title="variable">res</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d'"><span class="id" title="variable">d'</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.simrel.AbstractData.html#data_inject"><span class="id" title="method">data_inject</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</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.simrel.AbstractData.html#data_inv"><span class="id" title="method">data_inv</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d"><span class="id" title="variable">d</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.simrel.AbstractData.html#data_inject"><span class="id" title="method">data_inject</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d'"><span class="id" title="variable">d'</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#d'"><span class="id" title="variable">d'</span></a><br/>
}.<br/>
<br/>
<span class="id" title="keyword">Global Instance</span> <a name="gensem_to_cprimitive_preserves_invariant"><span class="id" title="instance">gensem_to_cprimitive_preserves_invariant</span></a><br/>
(<span class="id" title="var">D</span>: <a class="idref" href="liblayers.simrel.AbstractData.html#layerdata"><span class="id" title="record">layerdata</span></a>) {<span class="id" title="var">T</span>: <span class="id" title="keyword">Type</span>}<br/>
{<span class="id" title="var">targs</span> <span class="id" title="var">tres</span>}<br/>
`{<span class="id" title="var">semof_ops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semof"><span class="id" title="class">GenSem.Semof</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#targs"><span class="id" title="variable">targs</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#tres"><span class="id" title="variable">tres</span></a>}<br/>
{<span class="id" title="var">semprops</span>: <a class="idref" href="liblayers.compcertx.GenSem.html#Semprops"><span class="id" title="class">Semprops</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>}<br/>
(<span class="id" title="var">f</span>: <a class="idref" href="liblayers.compcertx.CGenSem.html#T"><span class="id" title="variable">T</span></a>):<br/>
<a class="idref" href="liblayers.compcertx.CGenSem.html#GenSemPreservesInvariant"><span class="id" title="class">GenSemPreservesInvariant</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#f"><span class="id" title="variable">f</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.CPrimitives.html#CPrimitivePreservesInvariant"><span class="id" title="class">CPrimitivePreservesInvariant</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> (<a class="idref" href="liblayers.compcertx.CGenSem.html#cgensem"><span class="id" title="definition">cgensem</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="liblayers.compcertx.CGenSem.html#f"><span class="id" title="variable">f</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">inversion</span> 1; <span class="id" title="tactic">subst</span>.<br/>
+ <span class="id" title="tactic">inversion</span> 1; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="tactic">eapply</span> <a class="idref" href="liblayers.compcertx.CGenSem.html#gensem_preserves_invariant_data_inv"><span class="id" title="method">gensem_preserves_invariant_data_inv</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
- <span class="id" title="tactic">eapply</span> <a class="idref" href="liblayers.compcertx.CGenSem.html#gensem_preserves_invariant_data_inject"><span class="id" title="method">gensem_preserves_invariant_data_inject</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
- <span class="id" title="tactic">eapply</span> <a class="idref" href="liblayers.compcertx.GenSem.html#semprops_inject_neutral"><span class="id" title="method">semprops_inject_neutral</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
+ <span class="id" title="tactic">intros</span>; <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.CGenSem.html#WITHMEM"><span class="id" title="section">WITHMEM</span></a>.<br/>
<br/>
<span class="id" title="keyword">Ltac</span> <span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span> :=<br/>
<span class="id" title="keyword">lazymatch</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/>
<br/>
</div>
<div class="doc">
FIXME: probably not the right number of arguments
</div>
<div class="code">
| <a class="idref" href="compcert.common.Events.html#external_call"><span class="id" title="definition">external_call</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> ⇒<br/>
<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="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof"><span class="id" title="definition">semof</span></a> ?<span class="id" title="var">f</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/>
<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.GenSem.html#semof"><span class="id" title="definition">semof</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_void"><span class="id" title="inductive">semof_nil_void</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/>
<br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">f</span> := <span class="id" title="tactic">fresh</span> "f" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d</span> := <span class="id" title="tactic">fresh</span> "d" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d'</span> := <span class="id" title="tactic">fresh</span> "d'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hfd</span> := <span class="id" title="tactic">fresh</span> "Hfd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hf</span> := <span class="id" title="tactic">fresh</span> "Hf" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hargs</span> := <span class="id" title="tactic">fresh</span> "Hargs" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd</span> := <span class="id" title="tactic">fresh</span> "Hd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hv</span> := <span class="id" title="tactic">fresh</span> "Hv" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd'</span> := <span class="id" title="tactic">fresh</span> "Hd'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> [<span class="id" title="var">f</span> <span class="id" title="var">d</span> <span class="id" title="var">d'</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">Hf</span> <span class="id" title="var">Hargs</span> <span class="id" title="var">Hd</span> <span class="id" title="var">Hv</span> <span class="id" title="var">Hd'</span>];<br/>
<span class="id" title="tactic">subst</span>;<br/>
<span class="id" title="tactic">clear</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="tactic">rename</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">into</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int"><span class="id" title="inductive">semof_nil_int</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/>
<br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">f</span> := <span class="id" title="tactic">fresh</span> "f" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d</span> := <span class="id" title="tactic">fresh</span> "d" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">z</span> := <span class="id" title="tactic">fresh</span> "z" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d'</span> := <span class="id" title="tactic">fresh</span> "d'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hfd</span> := <span class="id" title="tactic">fresh</span> "Hfd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hf</span> := <span class="id" title="tactic">fresh</span> "Hf" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hargs</span> := <span class="id" title="tactic">fresh</span> "Hargs" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd</span> := <span class="id" title="tactic">fresh</span> "Hd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hv</span> := <span class="id" title="tactic">fresh</span> "Hv" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd'</span> := <span class="id" title="tactic">fresh</span> "Hd'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> [<span class="id" title="var">f</span> <span class="id" title="var">d</span> <span class="id" title="var">z</span> <span class="id" title="var">d'</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">Hf</span> <span class="id" title="var">Hargs</span> <span class="id" title="var">Hd</span> <span class="id" title="var">Hv</span> <span class="id" title="var">Hd'</span>];<br/>
<span class="id" title="tactic">subst</span>;<br/>
<span class="id" title="tactic">clear</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="tactic">rename</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">into</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int_pure"><span class="id" title="instance">semof_nil_int_pure</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/>
<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int_pure"><span class="id" title="instance">semof_nil_int_pure</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int_pure_total"><span class="id" title="instance">semof_nil_int_pure_total</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/>
<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int_pure_total"><span class="id" title="instance">semof_nil_int_pure_total</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_cons"><span class="id" title="inductive">semof_cons</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/>
<br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">f</span> := <span class="id" title="tactic">fresh</span> "f" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">i</span> := <span class="id" title="tactic">fresh</span> "i" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">args</span> := <span class="id" title="tactic">fresh</span> "args" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d</span> := <span class="id" title="tactic">fresh</span> "d" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">v</span> := <span class="id" title="tactic">fresh</span> "v" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d'</span> := <span class="id" title="tactic">fresh</span> "d'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hfd</span> := <span class="id" title="tactic">fresh</span> "Hfd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hf</span> := <span class="id" title="tactic">fresh</span> "Hf" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hargs</span> := <span class="id" title="tactic">fresh</span> "Hargs" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd</span> := <span class="id" title="tactic">fresh</span> "Hd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hv</span> := <span class="id" title="tactic">fresh</span> "Hv" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd'</span> := <span class="id" title="tactic">fresh</span> "Hd'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> [<span class="id" title="var">f</span> <span class="id" title="var">i</span> <span class="id" title="var">args</span> <span class="id" title="var">d</span> <span class="id" title="var">v</span> <span class="id" title="var">d'</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">Hf</span> <span class="id" title="var">Hargs</span> <span class="id" title="var">Hd</span> <span class="id" title="var">Hv</span> <span class="id" title="var">Hd'</span>];<br/>
<span class="id" title="tactic">subst</span>;<br/>
<span class="id" title="tactic">clear</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="tactic">rename</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">into</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int64"><span class="id" title="inductive">semof_nil_int64</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/>
<br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">f</span> := <span class="id" title="tactic">fresh</span> "f" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d</span> := <span class="id" title="tactic">fresh</span> "d" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">z</span> := <span class="id" title="tactic">fresh</span> "z" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d'</span> := <span class="id" title="tactic">fresh</span> "d'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hfd</span> := <span class="id" title="tactic">fresh</span> "Hfd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hf</span> := <span class="id" title="tactic">fresh</span> "Hf" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hargs</span> := <span class="id" title="tactic">fresh</span> "Hargs" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd</span> := <span class="id" title="tactic">fresh</span> "Hd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hv</span> := <span class="id" title="tactic">fresh</span> "Hv" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd'</span> := <span class="id" title="tactic">fresh</span> "Hd'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> [<span class="id" title="var">f</span> <span class="id" title="var">d</span> <span class="id" title="var">z</span> <span class="id" title="var">d'</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">Hf</span> <span class="id" title="var">Hargs</span> <span class="id" title="var">Hd</span> <span class="id" title="var">Hv</span> <span class="id" title="var">Hd'</span>];<br/>
<span class="id" title="tactic">subst</span>;<br/>
<span class="id" title="tactic">clear</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="tactic">rename</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">into</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int64_pure"><span class="id" title="instance">semof_nil_int64_pure</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/>
<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int64_pure"><span class="id" title="instance">semof_nil_int64_pure</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int64_pure_total"><span class="id" title="instance">semof_nil_int64_pure_total</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/>
<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="liblayers.compcertx.GenSem.html#semof_nil_int64_pure_total"><span class="id" title="instance">semof_nil_int64_pure_total</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
| <a class="idref" href="liblayers.compcertx.GenSem.html#semof_cons64"><span class="id" title="inductive">semof_cons64</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/>
<br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">f</span> := <span class="id" title="tactic">fresh</span> "f" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">i</span> := <span class="id" title="tactic">fresh</span> "i" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">args</span> := <span class="id" title="tactic">fresh</span> "args" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d</span> := <span class="id" title="tactic">fresh</span> "d" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">v</span> := <span class="id" title="tactic">fresh</span> "v" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">d'</span> := <span class="id" title="tactic">fresh</span> "d'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hfd</span> := <span class="id" title="tactic">fresh</span> "Hfd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hf</span> := <span class="id" title="tactic">fresh</span> "Hf" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hargs</span> := <span class="id" title="tactic">fresh</span> "Hargs" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd</span> := <span class="id" title="tactic">fresh</span> "Hd" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hv</span> := <span class="id" title="tactic">fresh</span> "Hv" <span class="id" title="keyword">in</span><br/>
<span class="id" title="keyword">let</span> <span class="id" title="var">Hd'</span> := <span class="id" title="tactic">fresh</span> "Hd'" <span class="id" title="keyword">in</span><br/>
<span class="id" title="tactic">inversion</span> <span class="id" title="var">H</span> <span class="id" title="keyword">as</span> [<span class="id" title="var">f</span> <span class="id" title="var">i</span> <span class="id" title="var">args</span> <span class="id" title="var">d</span> <span class="id" title="var">v</span> <span class="id" title="var">d'</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">Hf</span> <span class="id" title="var">Hargs</span> <span class="id" title="var">Hd</span> <span class="id" title="var">Hv</span> <span class="id" title="var">Hd'</span>];<br/>
<span class="id" title="tactic">subst</span>;<br/>
<span class="id" title="tactic">clear</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="tactic">rename</span> <span class="id" title="var">Hfd</span> <span class="id" title="var">into</span> <span class="id" title="var">H</span>;<br/>
<span class="id" title="var">inv_generic_sem</span> <span class="id" title="var">H</span><br/>
<br/>
</div>
<div class="doc">
When all else fail, fall back on more generic inversion
tactics. This is useful not only as a base case, but sometimes
we mix generic semantics with manually defined ones in a given
layer, in which case it's more convenient if a single inversion
tactic works and yield similar results for both kinds.
</div>
<div class="code">
<br/>
| <span class="id" title="var">_</span> ⇒<br/>
<br/>
<span class="id" title="tactic">try</span> (<span class="id" title="var">inv_monad</span> <span class="id" title="var">H</span>);<br/>
<span class="id" title="tactic">try</span> <span class="id" title="var">inv</span> <span class="id" title="var">H</span><br/>
<br/>
<span class="id" title="keyword">end</span>.<br/>
</div>
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