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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>compcert.backend.SplitLongproof</title>
</head>
<body>
<div id="page">
<div id="header">
</div>
<div id="main">
<h1 class="libtitle">Library compcert.backend.SplitLongproof</h1>
<div class="code">
<br/>
</div>
<div class="doc">
Correctness of instruction selection for integer division
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Strings.String.html#"><span class="id" title="library">String</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="compcert.lib.Coqlib.html#"><span class="id" title="library">Coqlib</span></a> <a class="idref" href="compcert.lib.Maps.html#"><span class="id" title="library">Maps</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="compcert.common.AST.html#"><span class="id" title="library">AST</span></a> <a class="idref" href="compcert.common.Errors.html#"><span class="id" title="library">Errors</span></a> <a class="idref" href="compcert.lib.Integers.html#"><span class="id" title="library">Integers</span></a> <a class="idref" href="compcert.lib.Floats.html#"><span class="id" title="library">Floats</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="compcert.common.Values.html#"><span class="id" title="library">Values</span></a> <a class="idref" href="compcert.common.Memory.html#"><span class="id" title="library">Memory</span></a> <a class="idref" href="compcert.common.Globalenvs.html#"><span class="id" title="library">Globalenvs</span></a> <a class="idref" href="compcert.common.Events.html#"><span class="id" title="library">Events</span></a> <a class="idref" href="compcert.backend.Cminor.html#"><span class="id" title="library">Cminor</span></a> <a class="idref" href="compcert.x86.Op.html#"><span class="id" title="library">Op</span></a> <a class="idref" href="compcert.backend.CminorSel.html#"><span class="id" title="library">CminorSel</span></a>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="compcert.x86.SelectOp.html#"><span class="id" title="library">SelectOp</span></a> <a class="idref" href="compcert.x86.SelectOpproof.html#"><span class="id" title="library">SelectOpproof</span></a> <a class="idref" href="compcert.backend.SplitLong.html#"><span class="id" title="library">SplitLong</span></a>.<br/>
<br/>
<span class="id" title="keyword">Local Open</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">cminorsel_scope</span>.<br/>
<span class="id" title="keyword">Local Open</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">string_scope</span>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab556"></a><h1 class="section">Axiomatization of the helper functions</h1>
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Definition</span> <a name="external_implements"><span class="id" title="definition">external_implements</span></a><br/>
`{<span class="id" title="var">external_calls_ops</span>: <a class="idref" href="compcert.common.Events.html#ExternalCallsOps"><span class="id" title="class">ExternalCallsOps</span></a>}<br/>
(<span class="id" title="var">name</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Strings.String.html#string"><span class="id" title="inductive">string</span></a>) (<span class="id" title="var">sg</span>: <a class="idref" href="compcert.common.AST.html#signature"><span class="id" title="record">signature</span></a>) (<span class="id" title="var">vargs</span>: <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>) (<span class="id" title="var">vres</span>: <a class="idref" href="compcert.common.Values.html#val"><span class="id" title="inductive">val</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">F</span> <span class="id" title="var">V</span> (<span class="id" title="var">ge</span>: <a class="idref" href="compcert.common.Globalenvs.html#Genv.t"><span class="id" title="record">Genv.t</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#V"><span class="id" title="variable">V</span></a>) <span class="id" title="var">m</span>,<br/>
<a class="idref" href="compcert.common.Events.html#external_call"><span class="id" title="definition">external_call</span></a> (<a class="idref" href="compcert.common.AST.html#EF_runtime"><span class="id" title="constructor">EF_runtime</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vargs"><span class="id" title="variable">vargs</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.common.Events.html#E0"><span class="id" title="definition">E0</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#m"><span class="id" title="variable">m</span></a>.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="builtin_implements"><span class="id" title="definition">builtin_implements</span></a><br/>
`{<span class="id" title="var">external_calls_ops</span>: <a class="idref" href="compcert.common.Events.html#ExternalCallsOps"><span class="id" title="class">ExternalCallsOps</span></a>}<br/>
(<span class="id" title="var">name</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Strings.String.html#string"><span class="id" title="inductive">string</span></a>) (<span class="id" title="var">sg</span>: <a class="idref" href="compcert.common.AST.html#signature"><span class="id" title="record">signature</span></a>) (<span class="id" title="var">vargs</span>: <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>) (<span class="id" title="var">vres</span>: <a class="idref" href="compcert.common.Values.html#val"><span class="id" title="inductive">val</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">F</span> <span class="id" title="var">V</span> (<span class="id" title="var">ge</span>: <a class="idref" href="compcert.common.Globalenvs.html#Genv.t"><span class="id" title="record">Genv.t</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#V"><span class="id" title="variable">V</span></a>) <span class="id" title="var">m</span>,<br/>
<a class="idref" href="compcert.common.Events.html#external_call"><span class="id" title="definition">external_call</span></a> (<a class="idref" href="compcert.common.AST.html#EF_builtin"><span class="id" title="constructor">EF_builtin</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vargs"><span class="id" title="variable">vargs</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.common.Events.html#E0"><span class="id" title="definition">E0</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#m"><span class="id" title="variable">m</span></a>.<br/>
<br/>
<span class="id" title="keyword">Class</span> <a name="I64HelpersCorrect"><span class="id" title="record">I64HelpersCorrect</span></a> <span class="id" title="var">mem</span><br/>
`{<span class="id" title="var">external_calls_ops</span>: <a class="idref" href="compcert.common.Events.html#ExternalCallsOps"><span class="id" title="class">ExternalCallsOps</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#mem"><span class="id" title="variable">mem</span></a>} : <span class="id" title="keyword">Prop</span> :=<br/>
{<br/>
<a name="i64_helpers_correct"><span class="id" title="projection">i64_helpers_correct</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">x</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.longoffloat"><span class="id" title="definition">Val.longoffloat</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_dtos" <a class="idref" href="compcert.backend.SplitLong.html#sig_f_l"><span class="id" title="definition">sig_f_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.longuoffloat"><span class="id" title="definition">Val.longuoffloat</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_dtou" <a class="idref" href="compcert.backend.SplitLong.html#sig_f_l"><span class="id" title="definition">sig_f_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.floatoflong"><span class="id" title="definition">Val.floatoflong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_stod" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_f"><span class="id" title="definition">sig_l_f</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.floatoflongu"><span class="id" title="definition">Val.floatoflongu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_utod" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_f"><span class="id" title="definition">sig_l_f</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.singleoflong"><span class="id" title="definition">Val.singleoflong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_stof" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_s"><span class="id" title="definition">sig_l_s</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.singleoflongu"><span class="id" title="definition">Val.singleoflongu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_utof" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_s"><span class="id" title="definition">sig_l_s</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#builtin_implements"><span class="id" title="definition">builtin_implements</span></a> "__builtin_negl" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_l"><span class="id" title="definition">sig_l_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.negl"><span class="id" title="definition">Val.negl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#builtin_implements"><span class="id" title="definition">builtin_implements</span></a> "__builtin_addl" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.addl"><span class="id" title="definition">Val.addl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#builtin_implements"><span class="id" title="definition">builtin_implements</span></a> "__builtin_subl" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.subl"><span class="id" title="definition">Val.subl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#builtin_implements"><span class="id" title="definition">builtin_implements</span></a> "__builtin_mull" <a class="idref" href="compcert.backend.SplitLong.html#sig_ii_l"><span class="id" title="definition">sig_ii_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.mull'"><span class="id" title="definition">Val.mull'</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.divls"><span class="id" title="definition">Val.divls</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_sdiv" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.divlu"><span class="id" title="definition">Val.divlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_udiv" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.modls"><span class="id" title="definition">Val.modls</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_smod" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>, <a class="idref" href="compcert.common.Values.html#Val.modlu"><span class="id" title="definition">Val.modlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_umod" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_shl" <a class="idref" href="compcert.backend.SplitLong.html#sig_li_l"><span class="id" title="definition">sig_li_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.shll"><span class="id" title="definition">Val.shll</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_shr" <a class="idref" href="compcert.backend.SplitLong.html#sig_li_l"><span class="id" title="definition">sig_li_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.shrlu"><span class="id" title="definition">Val.shrlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_sar" <a class="idref" href="compcert.backend.SplitLong.html#sig_li_l"><span class="id" title="definition">sig_li_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.shrl"><span class="id" title="definition">Val.shrl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_umulh" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.mullhu"><span class="id" title="definition">Val.mullhu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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> <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">x</span> <span class="id" title="var">y</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> "__i64_smulh" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) (<a class="idref" href="compcert.common.Values.html#Val.mullhs"><span class="id" title="definition">Val.mullhs</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">)</span></a><br/>
}.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="helper_declared"><span class="id" title="definition">helper_declared</span></a> {<span class="id" title="var">F</span> <span class="id" title="var">V</span>: <span class="id" title="keyword">Type</span>} (<span class="id" title="var">p</span>: <a class="idref" href="compcert.common.AST.html#program"><span class="id" title="record">AST.program</span></a> (<a class="idref" href="compcert.common.AST.html#fundef"><span class="id" title="inductive">AST.fundef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#F"><span class="id" title="variable">F</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#V"><span class="id" title="variable">V</span></a>) (<span class="id" title="var">id</span>: <a class="idref" href="compcert.common.AST.html#ident"><span class="id" title="definition">ident</span></a>) (<span class="id" title="var">name</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Strings.String.html#string"><span class="id" title="inductive">string</span></a>) (<span class="id" title="var">sg</span>: <a class="idref" href="compcert.common.AST.html#signature"><span class="id" title="record">signature</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/>
<a class="idref" href="compcert.lib.Maps.html#e75e87027de4679a2bb49d0ac552f0e1"><span class="id" title="notation">(</span></a><a class="idref" href="compcert.common.AST.html#prog_defmap"><span class="id" title="definition">prog_defmap</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="compcert.lib.Maps.html#e75e87027de4679a2bb49d0ac552f0e1"><span class="id" title="notation">)!</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</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#Some"><span class="id" title="constructor">Some</span></a> (<a class="idref" href="compcert.common.AST.html#Gfun"><span class="id" title="constructor">Gfun</span></a> (<a class="idref" href="compcert.common.AST.html#External"><span class="id" title="constructor">External</span></a> (<a class="idref" href="compcert.common.AST.html#EF_runtime"><span class="id" title="constructor">EF_runtime</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a>))).<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="helper_functions_declared"><span class="id" title="definition">helper_functions_declared</span></a> {<span class="id" title="var">F</span> <span class="id" title="var">V</span>: <span class="id" title="keyword">Type</span>} (<span class="id" title="var">p</span>: <a class="idref" href="compcert.common.AST.html#program"><span class="id" title="record">AST.program</span></a> (<a class="idref" href="compcert.common.AST.html#fundef"><span class="id" title="inductive">AST.fundef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#F"><span class="id" title="variable">F</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#V"><span class="id" title="variable">V</span></a>) (<span class="id" title="var">hf</span>: <a class="idref" href="compcert.backend.SplitLong.html#helper_functions"><span class="id" title="class">helper_functions</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_dtos"><span class="id" title="method">i64_dtos</span></a> "__i64_dtos" <a class="idref" href="compcert.backend.SplitLong.html#sig_f_l"><span class="id" title="definition">sig_f_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_dtou"><span class="id" title="method">i64_dtou</span></a> "__i64_dtou" <a class="idref" href="compcert.backend.SplitLong.html#sig_f_l"><span class="id" title="definition">sig_f_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_stod"><span class="id" title="method">i64_stod</span></a> "__i64_stod" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_f"><span class="id" title="definition">sig_l_f</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_utod"><span class="id" title="method">i64_utod</span></a> "__i64_utod" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_f"><span class="id" title="definition">sig_l_f</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_stof"><span class="id" title="method">i64_stof</span></a> "__i64_stof" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_s"><span class="id" title="definition">sig_l_s</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_utof"><span class="id" title="method">i64_utof</span></a> "__i64_utof" <a class="idref" href="compcert.backend.SplitLong.html#sig_l_s"><span class="id" title="definition">sig_l_s</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_sdiv"><span class="id" title="method">i64_sdiv</span></a> "__i64_sdiv" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_udiv"><span class="id" title="method">i64_udiv</span></a> "__i64_udiv" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_smod"><span class="id" title="method">i64_smod</span></a> "__i64_smod" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_umod"><span class="id" title="method">i64_umod</span></a> "__i64_umod" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_shl"><span class="id" title="method">i64_shl</span></a> "__i64_shl" <a class="idref" href="compcert.backend.SplitLong.html#sig_li_l"><span class="id" title="definition">sig_li_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_shr"><span class="id" title="method">i64_shr</span></a> "__i64_shr" <a class="idref" href="compcert.backend.SplitLong.html#sig_li_l"><span class="id" title="definition">sig_li_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_sar"><span class="id" title="method">i64_sar</span></a> "__i64_sar" <a class="idref" href="compcert.backend.SplitLong.html#sig_li_l"><span class="id" title="definition">sig_li_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_umulh"><span class="id" title="method">i64_umulh</span></a> "__i64_umulh" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLong.html#i64_smulh"><span class="id" title="method">i64_smulh</span></a> "__i64_smulh" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a name="lab557"></a><h1 class="section">Correctness of the instruction selection functions for 64-bit operators</h1>
</div>
<div class="code">
<br/>
<span class="id" title="keyword">Section</span> <a name="CMCONSTR"><span class="id" title="section">CMCONSTR</span></a>.<br/>
<span class="id" title="keyword">Context</span> <span class="id" title="var">mem</span> `{<span class="id" title="var">external_calls_prf</span>: <a class="idref" href="compcert.common.Events.html#ExternalCalls"><span class="id" title="class">ExternalCalls</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#mem"><span class="id" title="variable">mem</span></a>}.<br/>
<span class="id" title="keyword">Context</span> `{<span class="id" title="var">i64_helpers_correct_prf</span>: !<a class="idref" href="compcert.backend.SplitLongproof.html#I64HelpersCorrect"><span class="id" title="class">I64HelpersCorrect</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.mem"><span class="id" title="variable">mem</span></a>}.<br/>
<br/>
<span class="id" title="keyword">Variable</span> <a name="CMCONSTR.prog"><span class="id" title="variable">prog</span></a>: <a class="idref" href="compcert.backend.CminorSel.html#program"><span class="id" title="definition">program</span></a>.<br/>
<span class="id" title="keyword">Variable</span> <a name="CMCONSTR.hf"><span class="id" title="variable">hf</span></a>: <a class="idref" href="compcert.backend.SplitLong.html#helper_functions"><span class="id" title="class">helper_functions</span></a>.<br/>
<span class="id" title="keyword">Hypothesis</span> <a name="CMCONSTR.HELPERS"><span class="id" title="variable">HELPERS</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#helper_functions_declared"><span class="id" title="definition">helper_functions_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.prog"><span class="id" title="variable">prog</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.hf"><span class="id" title="variable">hf</span></a>.<br/>
<span class="id" title="keyword">Let</span> <a name="CMCONSTR.ge"><span class="id" title="variable">ge</span></a> := <a class="idref" href="compcert.common.Globalenvs.html#Genv.globalenv"><span class="id" title="definition">Genv.globalenv</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.prog"><span class="id" title="variable">prog</span></a>.<br/>
<span class="id" title="keyword">Variable</span> <a name="CMCONSTR.sp"><span class="id" title="variable">sp</span></a>: <a class="idref" href="compcert.common.Values.html#val"><span class="id" title="inductive">val</span></a>.<br/>
<span class="id" title="keyword">Variable</span> <a name="CMCONSTR.e"><span class="id" title="variable">e</span></a>: <a class="idref" href="compcert.backend.Cminor.html#env"><span class="id" title="definition">env</span></a>.<br/>
<span class="id" title="keyword">Variable</span> <a name="CMCONSTR.m"><span class="id" title="variable">m</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.mem"><span class="id" title="variable">mem</span></a>.<br/>
<br/>
<span class="id" title="keyword">Ltac</span> <span class="id" title="var">UseHelper</span> := <span class="id" title="var">decompose</span> [<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#and"><span class="id" title="inductive">Logic.and</span></a>] <a class="idref" href="compcert.backend.SplitLongproof.html#i64_helpers_correct"><span class="id" title="method">i64_helpers_correct</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Ltac</span> <span class="id" title="var">DeclHelper</span> := <span class="id" title="tactic">red</span> <span class="id" title="keyword">in</span> <span class="id" title="var">HELPERS</span>; <span class="id" title="var">decompose</span> [<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#and"><span class="id" title="inductive">Logic.and</span></a>] <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.HELPERS"><span class="id" title="variable">HELPERS</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="eval_helper"><span class="id" title="lemma">eval_helper</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">id</span> <span class="id" title="var">name</span> <span class="id" title="var">sg</span> <span class="id" title="var">args</span> <span class="id" title="var">vargs</span> <span class="id" title="var">vres</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_exprlist"><span class="id" title="inductive">eval_exprlist</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#args"><span class="id" title="variable">args</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vargs"><span class="id" title="variable">vargs</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.prog"><span class="id" title="variable">prog</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vargs"><span class="id" title="variable">vargs</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eexternal"><span class="id" title="constructor">Eexternal</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#args"><span class="id" title="variable">args</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">red</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.common.Globalenvs.html#Genv.find_def_symbol"><span class="id" title="lemma">Genv.find_def_symbol</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">H0</span> <span class="id" title="keyword">as</span> (<span class="id" title="var">b</span> & <span class="id" title="var">P</span> & <span class="id" title="var">Q</span>).<br/>
<span class="id" title="tactic">rewrite</span> <- <a class="idref" href="compcert.common.Globalenvs.html#Genv.find_funct_ptr_iff"><span class="id" title="lemma">Genv.find_funct_ptr_iff</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">Q</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Corollary</span> <a name="eval_helper_1"><span class="id" title="lemma">eval_helper_1</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">id</span> <span class="id" title="var">name</span> <span class="id" title="var">sg</span> <span class="id" title="var">arg1</span> <span class="id" title="var">varg1</span> <span class="id" title="var">vres</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.prog"><span class="id" title="variable">prog</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eexternal"><span class="id" title="constructor">Eexternal</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper"><span class="id" title="lemma">eval_helper</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">constructor</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Corollary</span> <a name="eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">id</span> <span class="id" title="var">name</span> <span class="id" title="var">sg</span> <span class="id" title="var">arg1</span> <span class="id" title="var">arg2</span> <span class="id" title="var">varg1</span> <span class="id" title="var">varg2</span> <span class="id" title="var">vres</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg2"><span class="id" title="variable">arg2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#varg2"><span class="id" title="variable">varg2</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="compcert.backend.SplitLongproof.html#helper_declared"><span class="id" title="definition">helper_declared</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.prog"><span class="id" title="variable">prog</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</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="compcert.backend.SplitLongproof.html#external_implements"><span class="id" title="definition">external_implements</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#name"><span class="id" title="variable">name</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#varg2"><span class="id" title="variable">varg2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eexternal"><span class="id" title="constructor">Eexternal</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg2"><span class="id" title="variable">arg2</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper"><span class="id" title="lemma">eval_helper</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">constructor</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Remark</span> <a name="eval_builtin_1"><span class="id" title="lemma">eval_builtin_1</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">id</span> <span class="id" title="var">sg</span> <span class="id" title="var">arg1</span> <span class="id" title="var">varg1</span> <span class="id" title="var">vres</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</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="compcert.backend.SplitLongproof.html#builtin_implements"><span class="id" title="definition">builtin_implements</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Ebuiltin"><span class="id" title="constructor">Ebuiltin</span></a> (<a class="idref" href="compcert.common.AST.html#EF_builtin"><span class="id" title="constructor">EF_builtin</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a>) (<a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">econstructor</span>. <span class="id" title="tactic">econstructor</span>. <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">constructor</span>. <span class="id" title="tactic">apply</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Remark</span> <a name="eval_builtin_2"><span class="id" title="lemma">eval_builtin_2</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">id</span> <span class="id" title="var">sg</span> <span class="id" title="var">arg1</span> <span class="id" title="var">arg2</span> <span class="id" title="var">varg1</span> <span class="id" title="var">varg2</span> <span class="id" title="var">vres</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg2"><span class="id" title="variable">arg2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#varg2"><span class="id" title="variable">varg2</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="compcert.backend.SplitLongproof.html#builtin_implements"><span class="id" title="definition">builtin_implements</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#varg1"><span class="id" title="variable">varg1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="compcert.backend.SplitLongproof.html#varg2"><span class="id" title="variable">varg2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#0a8150c3c4df34d205c5ed9a427e2ed5"><span class="id" title="notation">::</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#nil"><span class="id" title="constructor">nil</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Ebuiltin"><span class="id" title="constructor">Ebuiltin</span></a> (<a class="idref" href="compcert.common.AST.html#EF_builtin"><span class="id" title="constructor">EF_builtin</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#id"><span class="id" title="variable">id</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#sg"><span class="id" title="variable">sg</span></a>) (<a class="idref" href="compcert.backend.SplitLongproof.html#arg1"><span class="id" title="variable">arg1</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#arg2"><span class="id" title="variable">arg2</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) <a class="idref" href="compcert.backend.SplitLongproof.html#vres"><span class="id" title="variable">vres</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">econstructor</span>. <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">constructor</span>. <span class="id" title="tactic">apply</span> <span class="id" title="var">H1</span>.<br/>
<span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> (<span class="id" title="var">cstr</span>: <a class="idref" href="compcert.backend.CminorSel.html#expr"><span class="id" title="inductive">expr</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="compcert.backend.CminorSel.html#expr"><span class="id" title="inductive">expr</span></a>) (<span class="id" title="var">sem</span>: <a class="idref" href="compcert.common.Values.html#val"><span class="id" title="inductive">val</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="compcert.common.Values.html#val"><span class="id" title="inductive">val</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#cstr"><span class="id" title="variable">cstr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a name="binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> (<span class="id" title="var">cstr</span>: <a class="idref" href="compcert.backend.CminorSel.html#expr"><span class="id" title="inductive">expr</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="compcert.backend.CminorSel.html#expr"><span class="id" title="inductive">expr</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="compcert.backend.CminorSel.html#expr"><span class="id" title="inductive">expr</span></a>) (<span class="id" title="var">sem</span>: <a class="idref" href="compcert.common.Values.html#val"><span class="id" title="inductive">val</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="compcert.common.Values.html#val"><span class="id" title="inductive">val</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="compcert.common.Values.html#val"><span class="id" title="inductive">val</span></a>) : <span class="id" title="keyword">Prop</span> :=<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">b</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#cstr"><span class="id" title="variable">cstr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<br/>
<span class="id" title="keyword">Ltac</span> <span class="id" title="var">EvalOp</span> :=<br/>
<span class="id" title="tactic">eauto</span>;<br/>
<span class="id" title="keyword">match</span> <span class="id" title="keyword">goal</span> <span class="id" title="keyword">with</span><br/>
| [ |- <a class="idref" href="compcert.backend.CminorSel.html#eval_exprlist"><span class="id" title="inductive">eval_exprlist</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> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a> <span class="id" title="var">_</span> ] ⇒ <span class="id" title="tactic">constructor</span><br/>
| [ |- <a class="idref" href="compcert.backend.CminorSel.html#eval_exprlist"><span class="id" title="inductive">eval_exprlist</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><a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a><span class="id" title="var">_</span>) <span class="id" title="var">_</span> ] ⇒ <span class="id" title="tactic">econstructor</span>; <span class="id" title="var">EvalOp</span><br/>
| [ |- <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</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> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">_</span> ] ⇒ <span class="id" title="tactic">constructor</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span><br/>
| [ |- <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</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> (<a class="idref" href="compcert.backend.CminorSel.html#Elet"><span class="id" title="constructor">Elet</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>) <span class="id" title="var">_</span> ] ⇒ <span class="id" title="tactic">econstructor</span>; <span class="id" title="var">EvalOp</span><br/>
| [ |- <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</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> (<a class="idref" href="compcert.backend.CminorSel.html#lift"><span class="id" title="definition">lift</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">_</span> ] ⇒ <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.CminorSel.html#eval_lift"><span class="id" title="lemma">eval_lift</span></a>; <span class="id" title="var">EvalOp</span><br/>
| [ |- <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> ] ⇒ <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.CminorSel.html#eval_Eop"><span class="id" title="constructor">eval_Eop</span></a>; [<span class="id" title="var">EvalOp</span> | <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span>]<br/>
| <span class="id" title="var">_</span> ⇒ <span class="id" title="tactic">idtac</span><br/>
<span class="id" title="keyword">end</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="eval_splitlong"><span class="id" title="lemma">eval_splitlong</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">f</span> <span class="id" title="var">v</span> <span class="id" title="var">sem</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">le</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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">p</span> <span class="id" title="var">q</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</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="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#q"><span class="id" title="variable">q</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="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.ofwords"><span class="id" title="definition">Int64.ofwords</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#q"><span class="id" title="variable">q</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#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">match</span> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a> <span class="id" title="keyword">with</span> <a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a> | <span class="id" title="var">_</span> ⇒ <a class="idref" href="compcert.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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.Values.html#Vundef"><span class="id" title="constructor">Vundef</span></a> <span class="id" title="keyword">end</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><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v'</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong"><span class="id" title="definition">splitlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v'"><span class="id" title="variable">v'</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v'"><span class="id" title="variable">v'</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">sem</span>; <span class="id" title="tactic">intros</span> <span class="id" title="var">EXEC</span> <span class="id" title="var">UNDEF</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#splitlong"><span class="id" title="definition">splitlong</span></a>. <span class="id" title="tactic">case</span> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong_match"><span class="id" title="definition">splitlong_match</span></a> <span class="id" title="var">a</span>); <span class="id" title="tactic">intros</span>.<br/>
- <span class="id" title="var">InvEval</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">exploit</span> <span class="id" title="var">EXEC</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H2</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v'</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v'</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> *; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v0</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> *; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="var">erewrite</span> <span class="id" title="var">B</span>; <span class="id" title="tactic">eauto</span>.<br/>
- <span class="id" title="var">exploit</span> (<span class="id" title="var">EXEC</span> (<span class="id" title="var">v</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">le</span>) (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Ohighlong"><span class="id" title="constructor">Ohighlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Olowlong"><span class="id" title="constructor">Olowlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>))).<br/>
<span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span> [<span class="id" title="var">v'</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v'</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>). <span class="id" title="var">erewrite</span> <span class="id" title="var">B</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>. <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="eval_splitlong_strict"><span class="id" title="lemma">eval_splitlong_strict</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">f</span> <span class="id" title="var">va</span> <span class="id" title="var">v</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</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">le</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.hiword"><span class="id" title="definition">Int64.hiword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.loword"><span class="id" title="definition">Int64.loword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong"><span class="id" title="definition">splitlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">v</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#splitlong"><span class="id" title="definition">splitlong</span></a>. <span class="id" title="tactic">case</span> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong_match"><span class="id" title="definition">splitlong_match</span></a> <span class="id" title="var">a</span>); <span class="id" title="tactic">intros</span>.<br/>
- <span class="id" title="var">InvEval</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>; <span class="id" title="tactic">try</span> <span class="id" title="tactic">discriminate</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">v0</span>; <span class="id" title="var">inv</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.hi_ofwords"><span class="id" title="lemma">Int64.hi_ofwords</span></a>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.lo_ofwords"><span class="id" title="lemma">Int64.lo_ofwords</span></a>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">EvalOp</span>. <span class="id" title="tactic">apply</span> <span class="id" title="var">H0</span>; <span class="id" title="var">EvalOp</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="eval_splitlong2"><span class="id" title="lemma">eval_splitlong2</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">f</span> <span class="id" title="var">va</span> <span class="id" title="var">vb</span> <span class="id" title="var">sem</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">le</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> <span class="id" title="var">x1</span> <span class="id" title="var">x2</span> <span class="id" title="var">y1</span> <span class="id" title="var">y2</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x1"><span class="id" title="variable">x1</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x2"><span class="id" title="variable">x2</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y1"><span class="id" title="variable">y1</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y2"><span class="id" title="variable">y2</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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b2"><span class="id" title="variable">b2</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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">p1</span> <span class="id" title="var">p2</span> <span class="id" title="var">q1</span> <span class="id" title="var">q2</span>,<br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#x1"><span class="id" title="variable">x1</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.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p1"><span class="id" title="variable">p1</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="compcert.backend.SplitLongproof.html#x2"><span class="id" title="variable">x2</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.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p2"><span class="id" title="variable">p2</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="compcert.backend.SplitLongproof.html#y1"><span class="id" title="variable">y1</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.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#q1"><span class="id" title="variable">q1</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="compcert.backend.SplitLongproof.html#y2"><span class="id" title="variable">y2</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.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#q2"><span class="id" title="variable">q2</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="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.ofwords"><span class="id" title="definition">Int64.ofwords</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#p2"><span class="id" title="variable">p2</span></a>)) (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.ofwords"><span class="id" title="definition">Int64.ofwords</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#q1"><span class="id" title="variable">q1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#q2"><span class="id" title="variable">q2</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#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">match</span> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</span></a>, <a class="idref" href="compcert.backend.SplitLongproof.html#vb"><span class="id" title="variable">vb</span></a> <span class="id" title="keyword">with</span> <a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <span class="id" title="var">_</span>, <a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a> | <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <a class="idref" href="compcert.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vb"><span class="id" title="variable">vb</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.Values.html#Vundef"><span class="id" title="constructor">Vundef</span></a> <span class="id" title="keyword">end</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><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vb"><span class="id" title="variable">vb</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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong2"><span class="id" title="definition">splitlong2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#sem"><span class="id" title="variable">sem</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vb"><span class="id" title="variable">vb</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">sem</span>; <span class="id" title="tactic">intros</span> <span class="id" title="var">EXEC</span> <span class="id" title="var">UNDEF</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#splitlong2"><span class="id" title="definition">splitlong2</span></a>. <span class="id" title="tactic">case</span> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong2_match"><span class="id" title="definition">splitlong2_match</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">intros</span>.<br/>
- <span class="id" title="var">InvEval</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">exploit</span> (<span class="id" title="var">EXEC</span> <span class="id" title="var">le</span> <span class="id" title="var">h1</span> <span class="id" title="var">l1</span> <span class="id" title="var">h2</span> <span class="id" title="var">l2</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> *; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v0</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v2</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> *; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v3</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="var">erewrite</span> <span class="id" title="var">B</span>; <span class="id" title="tactic">eauto</span>.<br/>
- <span class="id" title="var">InvEval</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">exploit</span> (<span class="id" title="var">EXEC</span> (<span class="id" title="var">vb</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">le</span>) (<a class="idref" href="compcert.backend.CminorSel.html#lift"><span class="id" title="definition">lift</span></a> <span class="id" title="var">h1</span>) (<a class="idref" href="compcert.backend.CminorSel.html#lift"><span class="id" title="definition">lift</span></a> <span class="id" title="var">l1</span>)<br/>
(<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Ohighlong"><span class="id" title="constructor">Ohighlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Olowlong"><span class="id" title="constructor">Olowlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>))).<br/>
<span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span> [<span class="id" title="var">v</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> *; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v0</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">vb</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="var">erewrite</span> <span class="id" title="var">B</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>. <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">InvEval</span>; <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="var">exploit</span> (<span class="id" title="var">EXEC</span> (<span class="id" title="var">va</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">le</span>)<br/>
(<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Ohighlong"><span class="id" title="constructor">Ohighlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Olowlong"><span class="id" title="constructor">Olowlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>))<br/>
(<a class="idref" href="compcert.backend.CminorSel.html#lift"><span class="id" title="definition">lift</span></a> <span class="id" title="var">h2</span>) (<a class="idref" href="compcert.backend.CminorSel.html#lift"><span class="id" title="definition">lift</span></a> <span class="id" title="var">l2</span>)).<br/>
<span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span> [<span class="id" title="var">v</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">va</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> *; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v0</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="var">erewrite</span> <span class="id" title="var">B</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>. <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">exploit</span> (<span class="id" title="var">EXEC</span> (<span class="id" title="var">vb</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">va</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">le</span>)<br/>
(<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Ohighlong"><span class="id" title="constructor">Ohighlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 1 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Olowlong"><span class="id" title="constructor">Olowlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 1 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>))<br/>
(<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Ohighlong"><span class="id" title="constructor">Ohighlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Olowlong"><span class="id" title="constructor">Olowlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0 <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>))).<br/>
<span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span> [<span class="id" title="var">v</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">va</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>); <span class="id" title="tactic">destruct</span> <span class="id" title="var">vb</span>; <span class="id" title="tactic">try</span> (<span class="id" title="tactic">rewrite</span> <span class="id" title="var">UNDEF</span>; <span class="id" title="tactic">auto</span>).<br/>
<span class="id" title="var">erewrite</span> <span class="id" title="var">B</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">rewrite</span> ! <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>; <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="eval_splitlong2_strict"><span class="id" title="lemma">eval_splitlong2_strict</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">f</span> <span class="id" title="var">va</span> <span class="id" title="var">vb</span> <span class="id" title="var">v</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vb"><span class="id" title="variable">vb</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">le</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.hiword"><span class="id" title="definition">Int64.hiword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.loword"><span class="id" title="definition">Int64.loword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#va"><span class="id" title="variable">va</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b1"><span class="id" title="variable">b1</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.hiword"><span class="id" title="definition">Int64.hiword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vb"><span class="id" title="variable">vb</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b2"><span class="id" title="variable">b2</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int64.loword"><span class="id" title="definition">Int64.loword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#vb"><span class="id" title="variable">vb</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b2"><span class="id" title="variable">b2</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong2"><span class="id" title="definition">splitlong2</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#f"><span class="id" title="variable">f</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">INV</span>: <span class="id" title="keyword">∀</span> <span class="id" title="var">v1</span> <span class="id" title="var">v2</span> <span class="id" title="var">n</span>,<br/>
<a class="idref" href="compcert.common.Values.html#Val.longofwords"><span class="id" title="definition">Val.longofwords</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v1"><span class="id" title="variable">v1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.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#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</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="compcert.backend.SplitLongproof.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#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a>(<a class="idref" href="compcert.lib.Integers.html#Int64.hiword"><span class="id" title="definition">Int64.hiword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</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="compcert.backend.SplitLongproof.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#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a>(<a class="idref" href="compcert.lib.Integers.html#Int64.loword"><span class="id" title="definition">Int64.loword</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)).<br/>
{<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H</span>; <span class="id" title="tactic">try</span> <span class="id" title="tactic">discriminate</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">v2</span>; <span class="id" title="var">inv</span> <span class="id" title="var">H</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.hi_ofwords"><span class="id" title="lemma">Int64.hi_ofwords</span></a>; <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.lo_ofwords"><span class="id" title="lemma">Int64.lo_ofwords</span></a>; <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">v</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#splitlong2"><span class="id" title="definition">splitlong2</span></a>. <span class="id" title="tactic">case</span> (<a class="idref" href="compcert.backend.SplitLong.html#splitlong2_match"><span class="id" title="definition">splitlong2_match</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">intros</span>.<br/>
- <span class="id" title="var">InvEval</span>. <span class="id" title="var">exploit</span> <span class="id" title="var">INV</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">EQ1</span> <span class="id" title="var">EQ2</span>]. <span class="id" title="var">exploit</span> <span class="id" title="var">INV</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">EQ3</span> <span class="id" title="var">EQ4</span>].<br/>
<span class="id" title="tactic">subst</span>. <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">InvEval</span>. <span class="id" title="var">exploit</span> <span class="id" title="var">INV</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">EQ1</span> <span class="id" title="var">EQ2</span>]. <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">econstructor</span>. <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">apply</span> <span class="id" title="var">H1</span>; <span class="id" title="var">EvalOp</span>.<br/>
- <span class="id" title="var">InvEval</span>. <span class="id" title="var">exploit</span> <span class="id" title="var">INV</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">EQ1</span> <span class="id" title="var">EQ2</span>]. <span class="id" title="tactic">subst</span>.<br/>
<span class="id" title="tactic">econstructor</span>. <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">apply</span> <span class="id" title="var">H1</span>; <span class="id" title="var">EvalOp</span>.<br/>
- <span class="id" title="var">EvalOp</span>. <span class="id" title="tactic">apply</span> <span class="id" title="var">H1</span>; <span class="id" title="var">EvalOp</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">n</span>,<br/>
<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</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#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a>; <span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">n</span>; <span class="id" title="tactic">intros</span> <span class="id" title="var">LC</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst_match"><span class="id" title="definition">is_longconst_match</span></a> <span class="id" title="var">a</span>); <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">inv</span> <span class="id" title="var">LC</span>. <span class="id" title="var">InvEval</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H5</span>. <span class="id" title="var">inv</span> <span class="id" title="var">H5</span>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">discriminate</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="is_longconst_zero_sound"><span class="id" title="lemma">is_longconst_zero_sound</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span>,<br/>
<a class="idref" href="compcert.backend.SplitLong.html#is_longconst_zero"><span class="id" title="definition">is_longconst_zero</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#is_longconst_zero"><span class="id" title="definition">is_longconst_zero</span></a>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">a</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">n</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">E</span>; <span class="id" title="tactic">try</span> <span class="id" title="tactic">discriminate</span>.<br/>
<span class="id" title="var">revert</span> <span class="id" title="var">H</span>. <span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int64.eq"><span class="id" title="definition">Int64.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.eq_spec"><span class="id" title="lemma">Int64.eq_spec</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">congruence</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="eval_lowlong"><span class="id" title="lemma">eval_lowlong</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#lowlong"><span class="id" title="definition">lowlong</span></a> <a class="idref" href="compcert.common.Values.html#Val.loword"><span class="id" title="definition">Val.loword</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#lowlong"><span class="id" title="definition">lowlong</span></a>; <span class="id" title="tactic">red</span>. <span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">x</span>. <span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#lowlong_match"><span class="id" title="definition">lowlong_match</span></a> <span class="id" title="var">a</span>); <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">InvEval</span>; <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">∃</span> <span class="id" title="var">v0</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">v0</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.lo_ofwords"><span class="id" title="lemma">Int64.lo_ofwords</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">∃</span> (<a class="idref" href="compcert.common.Values.html#Val.loword"><span class="id" title="definition">Val.loword</span></a> <span class="id" title="var">x</span>); <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="eval_highlong"><span class="id" title="lemma">eval_highlong</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#highlong"><span class="id" title="definition">highlong</span></a> <a class="idref" href="compcert.common.Values.html#Val.hiword"><span class="id" title="definition">Val.hiword</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#highlong"><span class="id" title="definition">highlong</span></a>; <span class="id" title="tactic">red</span>. <span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">x</span>. <span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#highlong_match"><span class="id" title="definition">highlong_match</span></a> <span class="id" title="var">a</span>); <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">InvEval</span>; <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">∃</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">v1</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">v0</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.hi_ofwords"><span class="id" title="lemma">Int64.hi_ofwords</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">∃</span> (<a class="idref" href="compcert.common.Values.html#Val.hiword"><span class="id" title="definition">Val.hiword</span></a> <span class="id" title="var">x</span>); <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a name="eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">n</span>, <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#longconst"><span class="id" title="definition">longconst</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>; <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="eval_intoflong"><span class="id" title="lemma">eval_intoflong</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#intoflong"><span class="id" title="definition">intoflong</span></a> <a class="idref" href="compcert.common.Values.html#Val.loword"><span class="id" title="definition">Val.loword</span></a>.<br/>
<span class="id" title="keyword">Proof</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_lowlong"><span class="id" title="lemma">eval_lowlong</span></a>.<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a name="eval_longofintu"><span class="id" title="lemma">eval_longofintu</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#longofintu"><span class="id" title="definition">longofintu</span></a> <a class="idref" href="compcert.common.Values.html#Val.longofintu"><span class="id" title="definition">Val.longofintu</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#longofintu"><span class="id" title="definition">longofintu</span></a>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.common.Values.html#Val.longofintu"><span class="id" title="definition">Val.longofintu</span></a>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">replace</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.repr"><span class="id" title="definition">Int64.repr</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <span class="id" title="var">i</span>)) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.ofwords"><span class="id" title="definition">Int64.ofwords</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</span></a> <span class="id" title="var">i</span>); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.lib.Integers.html#Int64.same_bits_eq"><span class="id" title="lemma">Int64.same_bits_eq</span></a>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.testbit_repr"><span class="id" title="lemma">Int64.testbit_repr</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.bits_ofwords"><span class="id" title="lemma">Int64.bits_ofwords</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">fold</span> (<a class="idref" href="compcert.lib.Integers.html#Int.testbit"><span class="id" title="definition">Int.testbit</span></a> <span class="id" title="var">i</span> <span class="id" title="var">i0</span>).<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Coqlib.html#zlt"><span class="id" title="definition">zlt</span></a> <span class="id" title="var">i0</span> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a>).<br/>
<span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.bits_zero"><span class="id" title="lemma">Int.bits_zero</span></a>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.bits_above"><span class="id" title="lemma">Int.bits_above</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">omega</span>. <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="eval_longofint"><span class="id" title="lemma">eval_longofint</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#longofint"><span class="id" title="definition">longofint</span></a> <a class="idref" href="compcert.common.Values.html#Val.longofint"><span class="id" title="definition">Val.longofint</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#longofint"><span class="id" title="definition">longofint</span></a>. <span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#longofint_match"><span class="id" title="definition">longofint_match</span></a> <span class="id" title="var">a</span>).<br/>
- <span class="id" title="var">InvEval</span>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>. <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.x86.SelectOpproof.html#eval_shrimm"><span class="id" title="lemma">eval_shrimm</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.repr"><span class="id" title="definition">Int.repr</span></a> 31) (<span class="id" title="var">x</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">le</span>) (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0)). <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span> [<span class="id" title="var">v1</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B</span>. <span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">replace</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.repr"><span class="id" title="definition">Int64.repr</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.signed"><span class="id" title="definition">Int.signed</span></a> <span class="id" title="var">i</span>))<br/>
<span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.ofwords"><span class="id" title="definition">Int64.ofwords</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.shr"><span class="id" title="definition">Int.shr</span></a> <span class="id" title="var">i</span> (<a class="idref" href="compcert.lib.Integers.html#Int.repr"><span class="id" title="definition">Int.repr</span></a> 31)) <span class="id" title="var">i</span>); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.lib.Integers.html#Int64.same_bits_eq"><span class="id" title="lemma">Int64.same_bits_eq</span></a>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.testbit_repr"><span class="id" title="lemma">Int64.testbit_repr</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.bits_ofwords"><span class="id" title="lemma">Int64.bits_ofwords</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.bits_signed"><span class="id" title="lemma">Int.bits_signed</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Coqlib.html#zlt"><span class="id" title="definition">zlt</span></a> <span class="id" title="var">i0</span> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a>).<br/>
<span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">assert</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.zwordsize"><span class="id" title="definition">Int64.zwordsize</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> 2 <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#88e34ed7a73f02772126289867960764"><span class="id" title="notation">×</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a>) <span class="id" title="tactic">by</span> <span class="id" title="tactic">reflexivity</span>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.bits_shr"><span class="id" title="lemma">Int.bits_shr</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.repr"><span class="id" title="definition">Int.repr</span></a> 31)) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#239a40728d107295b3cb2c790f57f9e9"><span class="id" title="notation">-</span></a> 1).<br/>
<span class="id" title="tactic">f_equal</span>. <span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Coqlib.html#zlt"><span class="id" title="definition">zlt</span></a> (<span class="id" title="var">i0</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#239a40728d107295b3cb2c790f57f9e9"><span class="id" title="notation">-</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#a3448b794f7a26d611ad36492b5d640b"><span class="id" title="notation">+</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#a3448b794f7a26d611ad36492b5d640b"><span class="id" title="notation">(</span></a><a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#239a40728d107295b3cb2c790f57f9e9"><span class="id" title="notation">-</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#a3448b794f7a26d611ad36492b5d640b"><span class="id" title="notation">)</span></a>) <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a>); <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a name="eval_negl"><span class="id" title="lemma">eval_negl</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#negl"><span class="id" title="definition">negl</span></a> <a class="idref" href="compcert.common.Values.html#Val.negl"><span class="id" title="definition">Val.negl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#negl"><span class="id" title="definition">negl</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">a</span>) <span class="id" title="var">eqn</span>:<span class="id" title="var">E</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">x</span>. <span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_builtin_1"><span class="id" title="lemma">eval_builtin_1</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">UseHelper</span>. <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="eval_notl"><span class="id" title="lemma">eval_notl</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#notl"><span class="id" title="definition">notl</span></a> <a class="idref" href="compcert.common.Values.html#Val.notl"><span class="id" title="definition">Val.notl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#notl"><span class="id" title="definition">notl</span></a>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong"><span class="id" title="lemma">eval_splitlong</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_notint"><span class="id" title="lemma">eval_notint</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">va</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_notint"><span class="id" title="lemma">eval_notint</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H1</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">vb</span> [<span class="id" title="var">C</span> <span class="id" title="var">D</span>]].<br/>
<span class="id" title="tactic">∃</span> (<a class="idref" href="compcert.common.Values.html#Val.longofwords"><span class="id" title="definition">Val.longofwords</span></a> <span class="id" title="var">va</span> <span class="id" title="var">vb</span>); <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="var">inv</span> <span class="id" title="var">B</span>; <span class="id" title="var">inv</span> <span class="id" title="var">D</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.lib.Integers.html#Int.not"><span class="id" title="definition">Int.not</span></a>. <span class="id" title="tactic">rewrite</span> <- <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_xor"><span class="id" title="lemma">Int64.decompose_xor</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <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="eval_longoffloat"><span class="id" title="lemma">eval_longoffloat</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.longoffloat"><span class="id" title="definition">Val.longoffloat</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#longoffloat"><span class="id" title="definition">longoffloat</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#longoffloat"><span class="id" title="definition">longoffloat</span></a>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_1"><span class="id" title="lemma">eval_helper_1</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_longuoffloat"><span class="id" title="lemma">eval_longuoffloat</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.longuoffloat"><span class="id" title="definition">Val.longuoffloat</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#longuoffloat"><span class="id" title="definition">longuoffloat</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#longuoffloat"><span class="id" title="definition">longuoffloat</span></a>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_1"><span class="id" title="lemma">eval_helper_1</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_floatoflong"><span class="id" title="lemma">eval_floatoflong</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.floatoflong"><span class="id" title="definition">Val.floatoflong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#floatoflong"><span class="id" title="definition">floatoflong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#floatoflong"><span class="id" title="definition">floatoflong</span></a>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_1"><span class="id" title="lemma">eval_helper_1</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_floatoflongu"><span class="id" title="lemma">eval_floatoflongu</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.floatoflongu"><span class="id" title="definition">Val.floatoflongu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#floatoflongu"><span class="id" title="definition">floatoflongu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#floatoflongu"><span class="id" title="definition">floatoflongu</span></a>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_1"><span class="id" title="lemma">eval_helper_1</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_longofsingle"><span class="id" title="lemma">eval_longofsingle</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.longofsingle"><span class="id" title="definition">Val.longofsingle</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#longofsingle"><span class="id" title="definition">longofsingle</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#longofsingle"><span class="id" title="definition">longofsingle</span></a>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>; <span class="id" title="var">inv</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Floats.html#Float32.to_long"><span class="id" title="definition">Float32.to_long</span></a> <span class="id" title="var">f</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">n</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">EQ</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H2</span>; <span class="id" title="var">inv</span> <span class="id" title="var">H2</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_floatofsingle"><span class="id" title="lemma">eval_floatofsingle</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> (<span class="id" title="var">v</span> & <span class="id" title="var">A</span> & <span class="id" title="var">B</span>). <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.lib.Floats.html#Float32.to_long_double"><span class="id" title="lemma">Float32.to_long_double</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">EQ</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longoffloat"><span class="id" title="lemma">eval_longoffloat</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Floats.html#Float.of_single"><span class="id" title="definition">Float.of_single</span></a> <span class="id" title="var">f</span>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Floats.html#Float32.to_double"><span class="id" title="definition">Float32.to_double</span></a> <span class="id" title="var">f</span>); <span class="id" title="tactic">rewrite</span> <span class="id" title="var">EQ</span>; <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="eval_longuofsingle"><span class="id" title="lemma">eval_longuofsingle</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.longuofsingle"><span class="id" title="definition">Val.longuofsingle</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#longuofsingle"><span class="id" title="definition">longuofsingle</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#longuofsingle"><span class="id" title="definition">longuofsingle</span></a>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H0</span>; <span class="id" title="var">inv</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Floats.html#Float32.to_longu"><span class="id" title="definition">Float32.to_longu</span></a> <span class="id" title="var">f</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">n</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">EQ</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">H2</span>; <span class="id" title="var">inv</span> <span class="id" title="var">H2</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_floatofsingle"><span class="id" title="lemma">eval_floatofsingle</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> (<span class="id" title="var">v</span> & <span class="id" title="var">A</span> & <span class="id" title="var">B</span>). <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.lib.Floats.html#Float32.to_longu_double"><span class="id" title="lemma">Float32.to_longu_double</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">EQ</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longuoffloat"><span class="id" title="lemma">eval_longuoffloat</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Floats.html#Float.of_single"><span class="id" title="definition">Float.of_single</span></a> <span class="id" title="var">f</span>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Floats.html#Float32.to_double"><span class="id" title="definition">Float32.to_double</span></a> <span class="id" title="var">f</span>); <span class="id" title="tactic">rewrite</span> <span class="id" title="var">EQ</span>; <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="eval_singleoflong"><span class="id" title="lemma">eval_singleoflong</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.singleoflong"><span class="id" title="definition">Val.singleoflong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#singleoflong"><span class="id" title="definition">singleoflong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#singleoflong"><span class="id" title="definition">singleoflong</span></a>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_1"><span class="id" title="lemma">eval_helper_1</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_singleoflongu"><span class="id" title="lemma">eval_singleoflongu</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.singleoflongu"><span class="id" title="definition">Val.singleoflongu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#singleoflongu"><span class="id" title="definition">singleoflongu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#singleoflongu"><span class="id" title="definition">singleoflongu</span></a>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_1"><span class="id" title="lemma">eval_helper_1</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_andl"><span class="id" title="lemma">eval_andl</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#andl"><span class="id" title="definition">andl</span></a> <a class="idref" href="compcert.common.Values.html#Val.andl"><span class="id" title="definition">Val.andl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#andl"><span class="id" title="definition">andl</span></a>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong2"><span class="id" title="lemma">eval_splitlong2</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_and"><span class="id" title="lemma">eval_and</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H1</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">va</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_and"><span class="id" title="lemma">eval_and</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H2</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">vb</span> [<span class="id" title="var">C</span> <span class="id" title="var">D</span>]].<br/>
<span class="id" title="tactic">∃</span> (<a class="idref" href="compcert.common.Values.html#Val.longofwords"><span class="id" title="definition">Val.longofwords</span></a> <span class="id" title="var">va</span> <span class="id" title="var">vb</span>); <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">D</span>; <span class="id" title="var">inv</span> <span class="id" title="var">D</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">f_equal</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_and"><span class="id" title="lemma">Int64.decompose_and</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">y</span>; <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="eval_orl"><span class="id" title="lemma">eval_orl</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#orl"><span class="id" title="definition">orl</span></a> <a class="idref" href="compcert.common.Values.html#Val.orl"><span class="id" title="definition">Val.orl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#orl"><span class="id" title="definition">orl</span></a>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong2"><span class="id" title="lemma">eval_splitlong2</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_or"><span class="id" title="lemma">eval_or</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H1</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">va</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_or"><span class="id" title="lemma">eval_or</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H2</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">vb</span> [<span class="id" title="var">C</span> <span class="id" title="var">D</span>]].<br/>
<span class="id" title="tactic">∃</span> (<a class="idref" href="compcert.common.Values.html#Val.longofwords"><span class="id" title="definition">Val.longofwords</span></a> <span class="id" title="var">va</span> <span class="id" title="var">vb</span>); <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">D</span>; <span class="id" title="var">inv</span> <span class="id" title="var">D</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">f_equal</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_or"><span class="id" title="lemma">Int64.decompose_or</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">y</span>; <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="eval_xorl"><span class="id" title="lemma">eval_xorl</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#xorl"><span class="id" title="definition">xorl</span></a> <a class="idref" href="compcert.common.Values.html#Val.xorl"><span class="id" title="definition">Val.xorl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#xorl"><span class="id" title="definition">xorl</span></a>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong2"><span class="id" title="lemma">eval_splitlong2</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_xor"><span class="id" title="lemma">eval_xor</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H1</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">va</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_xor"><span class="id" title="lemma">eval_xor</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H2</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">vb</span> [<span class="id" title="var">C</span> <span class="id" title="var">D</span>]].<br/>
<span class="id" title="tactic">∃</span> (<a class="idref" href="compcert.common.Values.html#Val.longofwords"><span class="id" title="definition">Val.longofwords</span></a> <span class="id" title="var">va</span> <span class="id" title="var">vb</span>); <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">D</span>; <span class="id" title="var">inv</span> <span class="id" title="var">D</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">f_equal</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_xor"><span class="id" title="lemma">Int64.decompose_xor</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">y</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="is_intconst_sound"><span class="id" title="lemma">is_intconst_sound</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">x</span> <span class="id" title="var">n</span>,<br/>
<a class="idref" href="compcert.backend.SplitLong.html#is_intconst"><span class="id" title="definition">is_intconst</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</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#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</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="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#is_intconst"><span class="id" title="definition">is_intconst</span></a>; <span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">n</span>; <span class="id" title="tactic">intros</span> <span class="id" title="var">LC</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">a</span>; <span class="id" title="tactic">try</span> <span class="id" title="tactic">discriminate</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">o</span>; <span class="id" title="tactic">try</span> <span class="id" title="tactic">discriminate</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">e0</span>; <span class="id" title="tactic">try</span> <span class="id" title="tactic">discriminate</span>.<br/>
<span class="id" title="var">inv</span> <span class="id" title="var">LC</span>. <span class="id" title="tactic">intros</span>. <span class="id" title="var">InvEval</span>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Remark</span> <a name="eval_shift_imm"><span class="id" title="lemma">eval_shift_imm</span></a>:<br/>
<span class="id" title="keyword">∀</span> (<span class="id" title="var">P</span>: <a class="idref" href="compcert.backend.CminorSel.html#expr"><span class="id" title="inductive">expr</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> <span class="id" title="keyword">Prop</span>) <span class="id" title="var">n</span> <span class="id" title="var">a0</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">a3</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><a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</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.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</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="compcert.backend.SplitLongproof.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a0"><span class="id" title="variable">a0</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>0 <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#cb2fd1306e4fe5d333fd9fb7e2c4a1d2"><span class="id" title="notation">≤</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#cb2fd1306e4fe5d333fd9fb7e2c4a1d2"><span class="id" title="notation"><</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</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="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="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="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="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="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="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="compcert.backend.SplitLongproof.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</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><a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#cb2fd1306e4fe5d333fd9fb7e2c4a1d2"><span class="id" title="notation">≤</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#cb2fd1306e4fe5d333fd9fb7e2c4a1d2"><span class="id" title="notation"><</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.zwordsize"><span class="id" title="definition">Int64.zwordsize</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="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a>) <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="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="compcert.backend.SplitLongproof.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</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="compcert.backend.SplitLongproof.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a3"><span class="id" title="variable">a3</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="compcert.backend.SplitLongproof.html#P"><span class="id" title="variable">P</span></a> (<span class="id" title="keyword">if</span> <a class="idref" href="compcert.lib.Integers.html#Int.eq"><span class="id" title="definition">Int.eq</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</span></a> <span class="id" title="keyword">then</span> <a class="idref" href="compcert.backend.SplitLongproof.html#a0"><span class="id" title="variable">a0</span></a><br/>
<span class="id" title="keyword">else</span> <span class="id" title="keyword">if</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <span class="id" title="keyword">then</span> <a class="idref" href="compcert.backend.SplitLongproof.html#a1"><span class="id" title="variable">a1</span></a><br/>
<span class="id" title="keyword">else</span> <span class="id" title="keyword">if</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a> <span class="id" title="keyword">then</span> <a class="idref" href="compcert.backend.SplitLongproof.html#a2"><span class="id" title="variable">a2</span></a><br/>
<span class="id" title="keyword">else</span> <a class="idref" href="compcert.backend.SplitLongproof.html#a3"><span class="id" title="variable">a3</span></a>).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="tactic">until</span> <span class="id" title="var">a3</span>; <span class="id" title="tactic">intros</span> <span class="id" title="var">A0</span> <span class="id" title="var">A1</span> <span class="id" title="var">A2</span> <span class="id" title="var">A3</span>.<br/>
<span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int.eq"><span class="id" title="definition">Int.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.eq_spec"><span class="id" title="lemma">Int.eq_spec</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</span></a>.<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">A0</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">NZ</span>: <a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <span class="id" title="var">n</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> 0).<br/>
{ <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">elim</span> <span class="id" title="var">H</span>. <span class="id" title="tactic">rewrite</span> <- (<a class="idref" href="compcert.lib.Integers.html#Int.repr_unsigned"><span class="id" title="lemma">Int.repr_unsigned</span></a> <span class="id" title="var">n</span>). <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H0</span>. <span class="id" title="tactic">auto</span>. }<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a>) <span class="id" title="var">eqn</span>:<span class="id" title="var">LT</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu_iwordsize_inv"><span class="id" title="lemma">Int.ltu_iwordsize_inv</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">RANGE</span>.<br/>
<span class="id" title="tactic">assert</span> (0 <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#cb2fd1306e4fe5d333fd9fb7e2c4a1d2"><span class="id" title="notation">≤</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#239a40728d107295b3cb2c790f57f9e9"><span class="id" title="notation">-</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <span class="id" title="var">n</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#cb2fd1306e4fe5d333fd9fb7e2c4a1d2"><span class="id" title="notation"><</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a>) <span class="id" title="tactic">by</span> <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">A1</span>. <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a>, <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned_repr_wordsize"><span class="id" title="lemma">Int.unsigned_repr_wordsize</span></a>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned_repr"><span class="id" title="lemma">Int.unsigned_repr</span></a>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Coqlib.html#zlt_true"><span class="id" title="lemma">zlt_true</span></a>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">generalize</span> <a class="idref" href="compcert.lib.Integers.html#Int.wordsize_max_unsigned"><span class="id" title="lemma">Int.wordsize_max_unsigned</span></a>; <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Coqlib.html#zlt_true"><span class="id" title="lemma">zlt_true</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a>) <span class="id" title="keyword">with</span> 64.<br/>
<span class="id" title="tactic">change</span> <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <span class="id" title="keyword">with</span> 32 <span class="id" title="keyword">in</span> <span class="id" title="var">RANGE</span>. <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a>) <span class="id" title="var">eqn</span>:<span class="id" title="var">LT'</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu_inv"><span class="id" title="lemma">Int.ltu_inv</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#88e34ed7a73f02772126289867960764"><span class="id" title="notation">×</span></a> 2).<br/>
<span class="id" title="tactic">intros</span> <span class="id" title="var">RANGE</span>.<br/>
<span class="id" title="tactic">assert</span> (<a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.ZArith.BinInt.html#208bafb0e148fe7fb7dcd812c227f4ee"><span class="id" title="notation">≤</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <span class="id" title="var">n</span>).<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">LT</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned_repr_wordsize"><span class="id" title="lemma">Int.unsigned_repr_wordsize</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">LT</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Coqlib.html#zlt"><span class="id" title="definition">zlt</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.unsigned"><span class="id" title="definition">Int.unsigned</span></a> <span class="id" title="var">n</span>) <a class="idref" href="compcert.lib.Integers.html#Int.zwordsize"><span class="id" title="definition">Int.zwordsize</span></a>). <span class="id" title="tactic">discriminate</span>. <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">apply</span> <span class="id" title="var">A2</span>. <span class="id" title="tactic">tauto</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a>, <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned_repr_wordsize"><span class="id" title="lemma">Int.unsigned_repr_wordsize</span></a>.<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int.unsigned_repr"><span class="id" title="lemma">Int.unsigned_repr</span></a>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Coqlib.html#zlt_true"><span class="id" title="lemma">zlt_true</span></a>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">omega</span>.<br/>
<span class="id" title="tactic">generalize</span> <a class="idref" href="compcert.lib.Integers.html#Int.wordsize_max_unsigned"><span class="id" title="lemma">Int.wordsize_max_unsigned</span></a>; <span class="id" title="tactic">omega</span>.<br/>
<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="eval_shllimm"><span class="id" title="lemma">eval_shllimm</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">n</span>,<br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">e</span> ⇒ <a class="idref" href="compcert.backend.SplitLong.html#shllimm"><span class="id" title="definition">shllimm</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">v</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.shll"><span class="id" title="definition">Val.shll</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#shllimm"><span class="id" title="definition">shllimm</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_shift_imm"><span class="id" title="lemma">eval_shift_imm</span></a>; <span class="id" title="tactic">intros</span>.<br/>
+ <br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">n</span>. <span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.shl'"><span class="id" title="definition">Int64.shl'</span></a> <span class="id" title="var">i</span> <a class="idref" href="compcert.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.shl"><span class="id" title="definition">Int64.shl</span></a> <span class="id" title="var">i</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>).<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.shl_zero"><span class="id" title="lemma">Int64.shl_zero</span></a>. <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong"><span class="id" title="lemma">eval_splitlong</span></a> <span class="id" title="keyword">with</span> (<span class="id" title="var">sem</span> := <span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.shll"><span class="id" title="definition">Val.shll</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <span class="id" title="var">n</span>)); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shlimm"><span class="id" title="lemma">eval_shlimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v1</span> [<span class="id" title="var">A1</span> <span class="id" title="var">B1</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shlimm"><span class="id" title="lemma">eval_shlimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H5</span>. <span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v2</span> [<span class="id" title="var">A2</span> <span class="id" title="var">B2</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shruimm"><span class="id" title="lemma">eval_shruimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H5</span>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v3</span> [<span class="id" title="var">A3</span> <span class="id" title="var">B3</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_or"><span class="id" title="lemma">eval_or</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A1</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v4</span> [<span class="id" title="var">A4</span> <span class="id" title="var">B4</span>]].<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H1</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H2</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H3</span>.<br/>
<span class="id" title="var">inv</span> <span class="id" title="var">B1</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B2</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B3</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B4</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B4</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_shl_1"><span class="id" title="lemma">Int64.decompose_shl_1</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_lowlong"><span class="id" title="lemma">eval_lowlong</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v1</span> [<span class="id" title="var">A1</span> <span class="id" title="var">B1</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shlimm"><span class="id" title="lemma">eval_shlimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A1</span>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v2</span> [<span class="id" title="var">A2</span> <span class="id" title="var">B2</span>]].<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a>); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B1</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B1</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B2</span>. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H1</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B2</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B2</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="var">erewrite</span> <- <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_shl_2"><span class="id" title="lemma">Int64.decompose_shl_2</span></a>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int64.hiword"><span class="id" title="definition">Int64.hiword</span></a> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>. <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_shll"><span class="id" title="lemma">eval_shll</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#shll"><span class="id" title="definition">shll</span></a> <a class="idref" href="compcert.common.Values.html#Val.shll"><span class="id" title="definition">Val.shll</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#shll"><span class="id" title="definition">shll</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_intconst"><span class="id" title="definition">is_intconst</span></a> <span class="id" title="var">b</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">n</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">IC</span>.<br/>
- <br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#is_intconst_sound"><span class="id" title="lemma">is_intconst_sound</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_shllimm"><span class="id" title="lemma">eval_shllimm</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
- <br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</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="eval_shrluimm"><span class="id" title="lemma">eval_shrluimm</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">n</span>,<br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">e</span> ⇒ <a class="idref" href="compcert.backend.SplitLong.html#shrluimm"><span class="id" title="definition">shrluimm</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">v</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.shrlu"><span class="id" title="definition">Val.shrlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#shrluimm"><span class="id" title="definition">shrluimm</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_shift_imm"><span class="id" title="lemma">eval_shift_imm</span></a>; <span class="id" title="tactic">intros</span>.<br/>
+ <br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">n</span>. <span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.shru'"><span class="id" title="definition">Int64.shru'</span></a> <span class="id" title="var">i</span> <a class="idref" href="compcert.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.shru"><span class="id" title="definition">Int64.shru</span></a> <span class="id" title="var">i</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>).<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.shru_zero"><span class="id" title="lemma">Int64.shru_zero</span></a>. <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong"><span class="id" title="lemma">eval_splitlong</span></a> <span class="id" title="keyword">with</span> (<span class="id" title="var">sem</span> := <span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.shrlu"><span class="id" title="definition">Val.shrlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <span class="id" title="var">n</span>)); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shruimm"><span class="id" title="lemma">eval_shruimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H5</span>. <span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v1</span> [<span class="id" title="var">A1</span> <span class="id" title="var">B1</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shruimm"><span class="id" title="lemma">eval_shruimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v2</span> [<span class="id" title="var">A2</span> <span class="id" title="var">B2</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shlimm"><span class="id" title="lemma">eval_shlimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v3</span> [<span class="id" title="var">A3</span> <span class="id" title="var">B3</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_or"><span class="id" title="lemma">eval_or</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A1</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v4</span> [<span class="id" title="var">A4</span> <span class="id" title="var">B4</span>]].<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H1</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H2</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H3</span>.<br/>
<span class="id" title="var">inv</span> <span class="id" title="var">B1</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B2</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B3</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B4</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B4</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_shru_1"><span class="id" title="lemma">Int64.decompose_shru_1</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_highlong"><span class="id" title="lemma">eval_highlong</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v1</span> [<span class="id" title="var">A1</span> <span class="id" title="var">B1</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shruimm"><span class="id" title="lemma">eval_shruimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A1</span>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v2</span> [<span class="id" title="var">A2</span> <span class="id" title="var">B2</span>]].<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a>); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B1</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B1</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B2</span>. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H1</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B2</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B2</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="var">erewrite</span> <- <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_shru_2"><span class="id" title="lemma">Int64.decompose_shru_2</span></a>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int64.loword"><span class="id" title="definition">Int64.loword</span></a> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>. <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_shrlu"><span class="id" title="lemma">eval_shrlu</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#shrlu"><span class="id" title="definition">shrlu</span></a> <a class="idref" href="compcert.common.Values.html#Val.shrlu"><span class="id" title="definition">Val.shrlu</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#shrlu"><span class="id" title="definition">shrlu</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_intconst"><span class="id" title="definition">is_intconst</span></a> <span class="id" title="var">b</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">n</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">IC</span>.<br/>
- <br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#is_intconst_sound"><span class="id" title="lemma">is_intconst_sound</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_shrluimm"><span class="id" title="lemma">eval_shrluimm</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
- <br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</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="eval_shrlimm"><span class="id" title="lemma">eval_shrlimm</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">n</span>,<br/>
<a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">e</span> ⇒ <a class="idref" href="compcert.backend.SplitLong.html#shrlimm"><span class="id" title="definition">shrlimm</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">v</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.shrl"><span class="id" title="definition">Val.shrl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#shrlimm"><span class="id" title="definition">shrlimm</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_shift_imm"><span class="id" title="lemma">eval_shift_imm</span></a>; <span class="id" title="tactic">intros</span>.<br/>
+ <br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">n</span>. <span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.shr'"><span class="id" title="definition">Int64.shr'</span></a> <span class="id" title="var">i</span> <a class="idref" href="compcert.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</span></a>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.shr"><span class="id" title="definition">Int64.shr</span></a> <span class="id" title="var">i</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>).<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.shr_zero"><span class="id" title="lemma">Int64.shr_zero</span></a>. <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong"><span class="id" title="lemma">eval_splitlong</span></a> <span class="id" title="keyword">with</span> (<span class="id" title="var">sem</span> := <span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.shrl"><span class="id" title="definition">Val.shrl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <span class="id" title="var">n</span>)); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shruimm"><span class="id" title="lemma">eval_shruimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H5</span>. <span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v1</span> [<span class="id" title="var">A1</span> <span class="id" title="var">B1</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shrimm"><span class="id" title="lemma">eval_shrimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v2</span> [<span class="id" title="var">A2</span> <span class="id" title="var">B2</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shlimm"><span class="id" title="lemma">eval_shlimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a> <span class="id" title="var">n</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v3</span> [<span class="id" title="var">A3</span> <span class="id" title="var">B3</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_or"><span class="id" title="lemma">eval_or</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A1</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v4</span> [<span class="id" title="var">A4</span> <span class="id" title="var">B4</span>]].<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">subst</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H1</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H2</span> <span class="id" title="keyword">in</span> ×. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H3</span>.<br/>
<span class="id" title="var">inv</span> <span class="id" title="var">B1</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B2</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B3</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B4</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B4</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_shr_1"><span class="id" title="lemma">Int64.decompose_shr_1</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_highlong"><span class="id" title="lemma">eval_highlong</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v1</span> [<span class="id" title="var">A1</span> <span class="id" title="var">B1</span>]].<br/>
<span class="id" title="tactic">assert</span> (<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> (<span class="id" title="var">v1</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">le</span>) (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0) <span class="id" title="var">v1</span>) <span class="id" title="tactic">by</span> <span class="id" title="var">EvalOp</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shrimm"><span class="id" title="lemma">eval_shrimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H2</span>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v2</span> [<span class="id" title="var">A2</span> <span class="id" title="var">B2</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_shrimm"><span class="id" title="lemma">eval_shrimm</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H2</span>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int.repr"><span class="id" title="definition">Int.repr</span></a> 31). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v3</span> [<span class="id" title="var">A3</span> <span class="id" title="var">B3</span>]].<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int64.iwordsize'"><span class="id" title="definition">Int64.iwordsize'</span></a>); <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B1</span>; <span class="id" title="var">inv</span> <span class="id" title="var">B1</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B2</span>. <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H1</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B2</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B2</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B3</span>. <span class="id" title="var">inv</span> <span class="id" title="var">B3</span>.<br/>
<span class="id" title="tactic">change</span> (<a class="idref" href="compcert.lib.Integers.html#Int.ltu"><span class="id" title="definition">Int.ltu</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.repr"><span class="id" title="definition">Int.repr</span></a> 31) <a class="idref" href="compcert.lib.Integers.html#Int.iwordsize"><span class="id" title="definition">Int.iwordsize</span></a>) <span class="id" title="keyword">with</span> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a>. <span class="id" title="tactic">simpl</span>.<br/>
<span class="id" title="var">erewrite</span> <- <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_shr_2"><span class="id" title="lemma">Int64.decompose_shr_2</span></a>. <span class="id" title="tactic">instantiate</span> (1 := <a class="idref" href="compcert.lib.Integers.html#Int64.loword"><span class="id" title="definition">Int64.loword</span></a> <span class="id" title="var">i</span>).<br/>
<span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.ofwords_recompose"><span class="id" title="lemma">Int64.ofwords_recompose</span></a>. <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">auto</span>.<br/>
+ <br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_shrl"><span class="id" title="lemma">eval_shrl</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#shrl"><span class="id" title="definition">shrl</span></a> <a class="idref" href="compcert.common.Values.html#Val.shrl"><span class="id" title="definition">Val.shrl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#shrl"><span class="id" title="definition">shrl</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_intconst"><span class="id" title="definition">is_intconst</span></a> <span class="id" title="var">b</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">n</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">IC</span>.<br/>
- <br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#is_intconst_sound"><span class="id" title="lemma">is_intconst_sound</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>; <span class="id" title="tactic">clear</span> <span class="id" title="var">H0</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_shrlimm"><span class="id" title="lemma">eval_shrlimm</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
- <br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_addl"><span class="id" title="lemma">eval_addl</span></a>: <a class="idref" href="compcert.x86_64.Archi.html#ptr64"><span class="id" title="definition">Archi.ptr64</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#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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#addl"><span class="id" title="definition">addl</span></a> <a class="idref" href="compcert.common.Values.html#Val.addl"><span class="id" title="definition">Val.addl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#addl"><span class="id" title="definition">addl</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">set</span> (<span class="id" title="var">default</span> := <a class="idref" href="compcert.backend.CminorSel.html#Ebuiltin"><span class="id" title="constructor">Ebuiltin</span></a> (<a class="idref" href="compcert.common.AST.html#EF_builtin"><span class="id" title="constructor">EF_builtin</span></a> "__builtin_addl" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a>) (<span class="id" title="var">a</span> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <span class="id" title="var">b</span> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)).<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">DEFAULT</span>:<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <span class="id" title="var">le</span> <span class="id" title="var">default</span> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.common.Values.html#Val.addl"><span class="id" title="definition">Val.addl</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>).<br/>
{<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_builtin_2"><span class="id" title="lemma">eval_builtin_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">UseHelper</span>. <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">a</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">p</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">LC1</span>;<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">b</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">q</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">LC2</span>.<br/>
- <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">a</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">x</span>.<br/>
<span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>. <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int64.eq"><span class="id" title="definition">Int64.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.eq_spec"><span class="id" title="lemma">Int64.eq_spec</span></a> <span class="id" title="var">p</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">p</span>. <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">a</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">x</span>.<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">y</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.common.Values.html#Val.addl"><span class="id" title="definition">Val.addl</span></a>; <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H</span>; <span class="id" title="tactic">destruct</span> <span class="id" title="var">y</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.add_zero_l"><span class="id" title="lemma">Int64.add_zero_l</span></a>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int64.eq"><span class="id" title="definition">Int64.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.eq_spec"><span class="id" title="lemma">Int64.eq_spec</span></a> <span class="id" title="var">q</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">q</span>. <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>.<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.common.Values.html#Val.addl"><span class="id" title="definition">Val.addl</span></a>; <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H</span>; <span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.add_zero"><span class="id" title="lemma">Int64.add_zero</span></a>; <span class="id" title="tactic">auto</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="eval_subl"><span class="id" title="lemma">eval_subl</span></a>: <a class="idref" href="compcert.x86_64.Archi.html#ptr64"><span class="id" title="definition">Archi.ptr64</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#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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#subl"><span class="id" title="definition">subl</span></a> <a class="idref" href="compcert.common.Values.html#Val.subl"><span class="id" title="definition">Val.subl</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#subl"><span class="id" title="definition">subl</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">set</span> (<span class="id" title="var">default</span> := <a class="idref" href="compcert.backend.CminorSel.html#Ebuiltin"><span class="id" title="constructor">Ebuiltin</span></a> (<a class="idref" href="compcert.common.AST.html#EF_builtin"><span class="id" title="constructor">EF_builtin</span></a> "__builtin_subl" <a class="idref" href="compcert.backend.SplitLong.html#sig_ll_l"><span class="id" title="definition">sig_ll_l</span></a>) (<span class="id" title="var">a</span> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <span class="id" title="var">b</span> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)).<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">DEFAULT</span>:<br/>
<a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <span class="id" title="var">le</span> <span class="id" title="var">default</span> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.common.Values.html#Val.subl"><span class="id" title="definition">Val.subl</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>).<br/>
{<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_builtin_2"><span class="id" title="lemma">eval_builtin_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">UseHelper</span>. <span class="id" title="tactic">auto</span>.<br/>
}<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">a</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">p</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">LC1</span>;<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">b</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">q</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">LC2</span>.<br/>
- <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">a</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">x</span>.<br/>
<span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>. <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int64.eq"><span class="id" title="definition">Int64.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.eq_spec"><span class="id" title="lemma">Int64.eq_spec</span></a> <span class="id" title="var">p</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">replace</span> (<a class="idref" href="compcert.common.Values.html#Val.subl"><span class="id" title="definition">Val.subl</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.common.Values.html#Val.negl"><span class="id" title="definition">Val.negl</span></a> <span class="id" title="var">y</span>). <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_negl"><span class="id" title="lemma">eval_negl</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">p</span>. <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">a</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">x</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">y</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int64.eq"><span class="id" title="definition">Int64.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.eq_spec"><span class="id" title="lemma">Int64.eq_spec</span></a> <span class="id" title="var">q</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">q</span>. <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>.<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.common.Values.html#Val.subl"><span class="id" title="definition">Val.subl</span></a>; <span class="id" title="tactic">rewrite</span> <span class="id" title="var">H</span>; <span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.sub_zero_l"><span class="id" title="lemma">Int64.sub_zero_l</span></a>; <span class="id" title="tactic">auto</span>.<br/>
- <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="eval_mull_base"><span class="id" title="lemma">eval_mull_base</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#mull_base"><span class="id" title="definition">mull_base</span></a> <a class="idref" href="compcert.common.Values.html#Val.mull"><span class="id" title="definition">Val.mull</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#mull_base"><span class="id" title="definition">mull_base</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_splitlong2"><span class="id" title="lemma">eval_splitlong2</span></a>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">set</span> (<span class="id" title="var">p</span> := <a class="idref" href="compcert.common.Values.html#Val.mull'"><span class="id" title="definition">Val.mull'</span></a> <span class="id" title="var">x2</span> <span class="id" title="var">y2</span>). <span class="id" title="tactic">set</span> (<span class="id" title="var">le1</span> := <span class="id" title="var">p</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">le0</span>).<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">E1</span>: <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <span class="id" title="var">le1</span> (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Olowlong"><span class="id" title="constructor">Olowlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#O"><span class="id" title="constructor">O</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) (<a class="idref" href="compcert.common.Values.html#Val.loword"><span class="id" title="definition">Val.loword</span></a> <span class="id" title="var">p</span>)) <span class="id" title="tactic">by</span> <span class="id" title="var">EvalOp</span>.<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">E2</span>: <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <span class="id" title="var">le1</span> (<a class="idref" href="compcert.backend.CminorSel.html#Eop"><span class="id" title="constructor">Eop</span></a> <a class="idref" href="compcert.x86.Op.html#Ohighlong"><span class="id" title="constructor">Ohighlong</span></a> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#O"><span class="id" title="constructor">O</span></a> <a class="idref" href="compcert.backend.CminorSel.html#a01f5d2bbf678cdb396f1debf5bc9771"><span class="id" title="notation">:::</span></a> <a class="idref" href="compcert.backend.CminorSel.html#Enil"><span class="id" title="constructor">Enil</span></a>)) (<a class="idref" href="compcert.common.Values.html#Val.hiword"><span class="id" title="definition">Val.hiword</span></a> <span class="id" title="var">p</span>)) <span class="id" title="tactic">by</span> <span class="id" title="var">EvalOp</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_mul"><span class="id" title="lemma">eval_mul</span></a>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.CminorSel.html#eval_lift"><span class="id" title="lemma">eval_lift</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H2</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.CminorSel.html#eval_lift"><span class="id" title="lemma">eval_lift</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H3</span>.<br/>
<span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">p</span>). <span class="id" title="tactic">fold</span> <span class="id" title="var">le1</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v3</span> [<span class="id" title="var">E3</span> <span class="id" title="var">L3</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_mul"><span class="id" title="lemma">eval_mul</span></a>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.CminorSel.html#eval_lift"><span class="id" title="lemma">eval_lift</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H1</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.CminorSel.html#eval_lift"><span class="id" title="lemma">eval_lift</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">H4</span>.<br/>
<span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">p</span>). <span class="id" title="tactic">fold</span> <span class="id" title="var">le1</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v4</span> [<span class="id" title="var">E4</span> <span class="id" title="var">L4</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_add"><span class="id" title="lemma">eval_add</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">E2</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">E3</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v5</span> [<span class="id" title="var">E5</span> <span class="id" title="var">L5</span>]].<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.x86.SelectOpproof.html#eval_add"><span class="id" title="lemma">eval_add</span></a>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">E5</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">E4</span>. <span class="id" title="tactic">intros</span> [<span class="id" title="var">v6</span> [<span class="id" title="var">E6</span> <span class="id" title="var">L6</span>]].<br/>
<span class="id" title="tactic">∃</span> (<a class="idref" href="compcert.common.Values.html#Val.longofwords"><span class="id" title="definition">Val.longofwords</span></a> <span class="id" title="var">v6</span> (<a class="idref" href="compcert.common.Values.html#Val.loword"><span class="id" title="definition">Val.loword</span></a> <span class="id" title="var">p</span>)); <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="keyword">Eval</span><span class="id" title="var">Op</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_builtin_2"><span class="id" title="lemma">eval_builtin_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">UseHelper</span>.<br/>
<span class="id" title="tactic">intros</span>. <span class="id" title="tactic">unfold</span> <span class="id" title="var">le1</span>, <span class="id" title="var">p</span> <span class="id" title="keyword">in</span> *; <span class="id" title="tactic">subst</span>; <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> ×.<br/>
<span class="id" title="var">inv</span> <span class="id" title="var">L3</span>. <span class="id" title="var">inv</span> <span class="id" title="var">L4</span>. <span class="id" title="var">inv</span> <span class="id" title="var">L5</span>. <span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">L6</span>. <span class="id" title="var">inv</span> <span class="id" title="var">L6</span>.<br/>
<span class="id" title="tactic">simpl</span>. <span class="id" title="tactic">f_equal</span>. <span class="id" title="tactic">symmetry</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.lib.Integers.html#Int64.decompose_mul"><span class="id" title="lemma">Int64.decompose_mul</span></a>.<br/>
- <span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>; <span class="id" title="tactic">destruct</span> <span class="id" title="var">y</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="eval_mullimm"><span class="id" title="lemma">eval_mullimm</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">n</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#mullimm"><span class="id" title="definition">mullimm</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">v</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.mull"><span class="id" title="definition">Val.mull</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#mullimm"><span class="id" title="definition">mullimm</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int64.eq"><span class="id" title="definition">Int64.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.eq_spec"><span class="id" title="lemma">Int64.eq_spec</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int64.zero"><span class="id" title="definition">Int64.zero</span></a>.<br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">n</span>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.mul_zero"><span class="id" title="lemma">Int64.mul_zero</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="var">predSpec</span> <a class="idref" href="compcert.lib.Integers.html#Int64.eq"><span class="id" title="definition">Int64.eq</span></a> <a class="idref" href="compcert.lib.Integers.html#Int64.eq_spec"><span class="id" title="lemma">Int64.eq_spec</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int64.one"><span class="id" title="definition">Int64.one</span></a>.<br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">n</span>. <span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.mul_one"><span class="id" title="lemma">Int64.mul_one</span></a>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Integers.html#Int64.is_power2'"><span class="id" title="definition">Int64.is_power2'</span></a> <span class="id" title="var">n</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">l</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">P2</span>.<br/>
<span class="id" title="var">exploit</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_shllimm"><span class="id" title="lemma">eval_shllimm</span></a>. <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">instantiate</span> (1 := <span class="id" title="var">l</span>). <span class="id" title="tactic">intros</span> [<span class="id" title="var">v</span> [<span class="id" title="var">A</span> <span class="id" title="var">B</span>]].<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="var">erewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.mul_pow2'"><span class="id" title="lemma">Int64.mul_pow2'</span></a> <span class="id" title="tactic">by</span> <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">simpl</span> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span>. <span class="id" title="var">erewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.is_power2'_range"><span class="id" title="lemma">Int64.is_power2'_range</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">B</span> <span class="id" title="tactic">by</span> <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">exact</span> <span class="id" title="var">B</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_mull_base"><span class="id" title="lemma">eval_mull_base</span></a>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a name="eval_mull"><span class="id" title="lemma">eval_mull</span></a>: <a class="idref" href="compcert.backend.SplitLongproof.html#binary_constructor_sound"><span class="id" title="definition">binary_constructor_sound</span></a> <a class="idref" href="compcert.backend.SplitLong.html#mull"><span class="id" title="definition">mull</span></a> <a class="idref" href="compcert.common.Values.html#Val.mull"><span class="id" title="definition">Val.mull</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#mull"><span class="id" title="definition">mull</span></a>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">a</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">p</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">LC1</span>;<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.backend.SplitLong.html#is_longconst"><span class="id" title="definition">is_longconst</span></a> <span class="id" title="var">b</span>) <span class="id" title="keyword">as</span> [<span class="id" title="var">q</span>|] <span class="id" title="var">eqn</span>:<span class="id" title="var">LC2</span>.<br/>
- <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">a</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">x</span>.<br/>
<span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>. <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">a</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">x</span>.<br/>
<span class="id" title="tactic">replace</span> (<a class="idref" href="compcert.common.Values.html#Val.mull"><span class="id" title="definition">Val.mull</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <span class="id" title="var">p</span>) <span class="id" title="var">y</span>) <span class="id" title="keyword">with</span> (<a class="idref" href="compcert.common.Values.html#Val.mull"><span class="id" title="definition">Val.mull</span></a> <span class="id" title="var">y</span> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <span class="id" title="var">p</span>)) <span class="id" title="keyword">in</span> ×.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_mullimm"><span class="id" title="lemma">eval_mullimm</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">destruct</span> <span class="id" title="var">y</span>; <span class="id" title="tactic">simpl</span>; <span class="id" title="tactic">auto</span>. <span class="id" title="tactic">rewrite</span> <a class="idref" href="compcert.lib.Integers.html#Int64.mul_commut"><span class="id" title="lemma">Int64.mul_commut</span></a>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="var">exploit</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#is_longconst_sound"><span class="id" title="lemma">is_longconst_sound</span></a> <span class="id" title="var">le</span> <span class="id" title="var">b</span>); <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">intros</span> <span class="id" title="var">EQ</span>; <span class="id" title="tactic">subst</span> <span class="id" title="var">y</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_mullimm"><span class="id" title="lemma">eval_mullimm</span></a>; <span class="id" title="tactic">eauto</span>.<br/>
- <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_mull_base"><span class="id" title="lemma">eval_mull_base</span></a>; <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="eval_mullhu"><span class="id" title="lemma">eval_mullhu</span></a>: <br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">n</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="compcert.backend.SplitLong.html#mullhu"><span class="id" title="definition">mullhu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">v</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.mullhu"><span class="id" title="definition">Val.mullhu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#mullhu"><span class="id" title="definition">mullhu</span></a>; <span class="id" title="tactic">intros</span>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>. <span class="id" title="var">DeclHelper</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">UseHelper</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a name="eval_mullhs"><span class="id" title="lemma">eval_mullhs</span></a>: <br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">n</span>, <a class="idref" href="compcert.backend.SplitLongproof.html#unary_constructor_sound"><span class="id" title="definition">unary_constructor_sound</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="compcert.backend.SplitLong.html#mullhs"><span class="id" title="definition">mullhs</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">v</span> ⇒ <a class="idref" href="compcert.common.Values.html#Val.mullhs"><span class="id" title="definition">Val.mullhs</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a> (<a class="idref" href="compcert.common.Values.html#Vlong"><span class="id" title="constructor">Vlong</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)).<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#mullhs"><span class="id" title="definition">mullhs</span></a>; <span class="id" title="tactic">intros</span>; <span class="id" title="tactic">red</span>; <span class="id" title="tactic">intros</span>. <span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_longconst"><span class="id" title="lemma">eval_longconst</span></a>. <span class="id" title="var">DeclHelper</span>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">UseHelper</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a name="eval_shrxlimm"><span class="id" title="lemma">eval_shrxlimm</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">n</span> <span class="id" title="var">x</span> <span class="id" title="var">z</span>,<br/>
<a class="idref" href="compcert.x86_64.Archi.html#ptr64"><span class="id" title="definition">Archi.ptr64</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#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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.shrxl"><span class="id" title="definition">Val.shrxl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</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#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#shrxlimm"><span class="id" title="definition">shrxlimm</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>.<br/>
<span class="id" title="tactic">apply</span> <a class="idref" href="compcert.common.Values.html#Val.shrxl_shrl_2"><span class="id" title="lemma">Val.shrxl_shrl_2</span></a> <span class="id" title="keyword">in</span> <span class="id" title="var">H1</span>. <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#shrxlimm"><span class="id" title="definition">shrxlimm</span></a>.<br/>
<span class="id" title="tactic">destruct</span> (<a class="idref" href="compcert.lib.Integers.html#Int.eq"><span class="id" title="definition">Int.eq</span></a> <span class="id" title="var">n</span> <a class="idref" href="compcert.lib.Integers.html#Int.zero"><span class="id" title="definition">Int.zero</span></a>).<br/>
- <span class="id" title="tactic">subst</span> <span class="id" title="var">z</span>; <span class="id" title="tactic">∃</span> <span class="id" title="var">x</span>; <span class="id" title="tactic">auto</span>.<br/>
- <span class="id" title="tactic">set</span> (<span class="id" title="var">le'</span> := <span class="id" title="var">x</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">le</span>).<br/>
<span class="id" title="var">edestruct</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#eval_shrlimm"><span class="id" title="lemma">eval_shrlimm</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.repr"><span class="id" title="definition">Int.repr</span></a> 63) <span class="id" title="var">le'</span> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#O"><span class="id" title="constructor">O</span></a>)) <span class="id" title="keyword">as</span> (<span class="id" title="var">v1</span> & <span class="id" title="var">A1</span> & <span class="id" title="var">B1</span>).<br/>
<span class="id" title="tactic">constructor</span>. <span class="id" title="tactic">reflexivity</span>.<br/>
<span class="id" title="var">edestruct</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#eval_shrluimm"><span class="id" title="lemma">eval_shrluimm</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.sub"><span class="id" title="definition">Int.sub</span></a> (<a class="idref" href="compcert.lib.Integers.html#Int.repr"><span class="id" title="definition">Int.repr</span></a> 64) <span class="id" title="var">n</span>) <span class="id" title="var">le'</span>) <span class="id" title="keyword">as</span> (<span class="id" title="var">v2</span> & <span class="id" title="var">A2</span> & <span class="id" title="var">B2</span>).<br/>
<span class="id" title="tactic">eexact</span> <span class="id" title="var">A1</span>.<br/>
<span class="id" title="var">edestruct</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#eval_addl"><span class="id" title="lemma">eval_addl</span></a> <span class="id" title="var">H</span> <span class="id" title="var">le'</span> (<a class="idref" href="compcert.backend.CminorSel.html#Eletvar"><span class="id" title="constructor">Eletvar</span></a> 0)) <span class="id" title="keyword">as</span> (<span class="id" title="var">v3</span> & <span class="id" title="var">A3</span> & <span class="id" title="var">B3</span>).<br/>
<span class="id" title="tactic">constructor</span>. <span class="id" title="tactic">reflexivity</span>. <span class="id" title="tactic">eexact</span> <span class="id" title="var">A2</span>.<br/>
<span class="id" title="var">edestruct</span> (<a class="idref" href="compcert.backend.SplitLongproof.html#eval_shrlimm"><span class="id" title="lemma">eval_shrlimm</span></a> <span class="id" title="var">n</span> <span class="id" title="var">le'</span>) <span class="id" title="keyword">as</span> (<span class="id" title="var">v4</span> & <span class="id" title="var">A4</span> & <span class="id" title="var">B4</span>). <span class="id" title="tactic">eexact</span> <span class="id" title="var">A3</span>.<br/>
<span class="id" title="tactic">∃</span> <span class="id" title="var">v4</span>; <span class="id" title="tactic">split</span>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">eauto</span>.<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">X</span>: <span class="id" title="keyword">∀</span> <span class="id" title="var">v1</span> <span class="id" title="var">v2</span> <span class="id" title="var">n</span>, <a class="idref" href="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v1"><span class="id" title="variable">v1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.common.Values.html#Val.shrl"><span class="id" title="definition">Val.shrl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v1"><span class="id" title="variable">v1</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)) (<a class="idref" href="compcert.common.Values.html#Val.shrl"><span class="id" title="definition">Val.shrl</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v2"><span class="id" title="variable">v2</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>))).<br/>
{ <span class="id" title="tactic">intros</span>. <span class="id" title="var">inv</span> <span class="id" title="var">H2</span>; <span class="id" title="tactic">auto</span>. }<br/>
<span class="id" title="tactic">assert</span> (<span class="id" title="var">Y</span>: <span class="id" title="keyword">∀</span> <span class="id" title="var">v1</span> <span class="id" title="var">v2</span> <span class="id" title="var">n</span>, <a class="idref" href="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v1"><span class="id" title="variable">v1</span></a> <a class="idref" href="compcert.backend.SplitLongproof.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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> (<a class="idref" href="compcert.common.Values.html#Val.shrlu"><span class="id" title="definition">Val.shrlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v1"><span class="id" title="variable">v1</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>)) (<a class="idref" href="compcert.common.Values.html#Val.shrlu"><span class="id" title="definition">Val.shrlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v2"><span class="id" title="variable">v2</span></a> (<a class="idref" href="compcert.common.Values.html#Vint"><span class="id" title="constructor">Vint</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#n"><span class="id" title="variable">n</span></a>))).<br/>
{ <span class="id" title="tactic">intros</span>. <span class="id" title="var">inv</span> <span class="id" title="var">H2</span>; <span class="id" title="tactic">auto</span>. }<br/>
<span class="id" title="tactic">subst</span> <span class="id" title="var">z</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.common.Values.html#Val.lessdef_trans"><span class="id" title="lemma">Val.lessdef_trans</span></a>; [|<span class="id" title="tactic">eexact</span> <span class="id" title="var">B4</span>]. <span class="id" title="tactic">apply</span> <span class="id" title="var">X</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.common.Values.html#Val.lessdef_trans"><span class="id" title="lemma">Val.lessdef_trans</span></a>; [|<span class="id" title="tactic">eexact</span> <span class="id" title="var">B3</span>]. <span class="id" title="tactic">apply</span> <a class="idref" href="compcert.common.Values.html#Val.addl_lessdef"><span class="id" title="lemma">Val.addl_lessdef</span></a>; <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.common.Values.html#Val.lessdef_trans"><span class="id" title="lemma">Val.lessdef_trans</span></a>; [|<span class="id" title="tactic">eexact</span> <span class="id" title="var">B2</span>]. <span class="id" title="tactic">apply</span> <span class="id" title="var">Y</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="eval_divlu_base"><span class="id" title="lemma">eval_divlu_base</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.divlu"><span class="id" title="definition">Val.divlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#divlu_base"><span class="id" title="definition">divlu_base</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#divlu_base"><span class="id" title="definition">divlu_base</span></a>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <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="eval_modlu_base"><span class="id" title="lemma">eval_modlu_base</span></a>:<br/>
<span class="id" title="keyword">∀</span> <span class="id" title="var">le</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span>,<br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
<a class="idref" href="compcert.common.Values.html#Val.modlu"><span class="id" title="definition">Val.modlu</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</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#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">∃</span></a> <span class="id" title="var">v</span><a class="idref" href="http://coq.inria.fr/distrib/8.6/stdlib/Coq.Init.Logic.html#84eb6d2849dbf3581b1c0c05add5f2d8"><span class="id" title="notation">,</span></a> <a class="idref" href="compcert.backend.CminorSel.html#eval_expr"><span class="id" title="inductive">eval_expr</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.ge"><span class="id" title="variable">ge</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.sp"><span class="id" title="variable">sp</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.e"><span class="id" title="variable">e</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#CMCONSTR.m"><span class="id" title="variable">m</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#le"><span class="id" title="variable">le</span></a> (<a class="idref" href="compcert.backend.SplitLong.html#modlu_base"><span class="id" title="definition">modlu_base</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#b"><span class="id" title="variable">b</span></a>) <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</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="compcert.common.Values.html#Val.lessdef"><span class="id" title="inductive">Val.lessdef</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="compcert.backend.SplitLongproof.html#v"><span class="id" title="variable">v</span></a>.<br/>
<span class="id" title="keyword">Proof</span>.<br/>
<span class="id" title="tactic">intros</span>; <span class="id" title="tactic">unfold</span> <a class="idref" href="compcert.backend.SplitLong.html#modlu_base"><span class="id" title="definition">modlu_base</span></a>.<br/>
<span class="id" title="tactic">econstructor</span>; <span class="id" title="tactic">split</span>. <span class="id" title="tactic">eapply</span> <a class="idref" href="compcert.backend.SplitLongproof.html#eval_helper_2"><span class="id" title="lemma">eval_helper_2</span></a>; <span class="id" title="tactic">eauto</span>. <span class="id" title="var">DeclHelper</span>. <span class="id" title="var">UseHelper</span>. <span class="id" title="tactic">auto</span>.<br/>
<span class="id" title="keyword">Qed</span>.<br/>