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| author | Yann Herklotz <git@yannherklotz.com> | 2020-11-26 01:00:41 +0000 |
|---|---|---|
| committer | Yann Herklotz <git@yannherklotz.com> | 2020-11-26 01:00:41 +0000 |
| commit | fa4b252945a870100305c159d20e264be18973ce (patch) | |
| tree | 435cbd07a2af45f3f08dc8ac892fa48044047eeb /docs/proof/Compiler.html | |
| parent | 29bee524cccfe08c680f655b1969a4c421e0a969 (diff) | |
| download | vericert-kvx-fa4b252945a870100305c159d20e264be18973ce.tar.gz vericert-kvx-fa4b252945a870100305c159d20e264be18973ce.zip | |
Add proof documentation
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diff --git a/docs/proof/Compiler.html b/docs/proof/Compiler.html new file mode 100644 index 0000000..fa9c633 --- /dev/null +++ b/docs/proof/Compiler.html @@ -0,0 +1,768 @@ +<?xml version="1.0" encoding="utf-8" ?> +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml" class="alectryon-standalone" xml:lang="en" lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> +<meta name="generator" content="Docutils 0.16: http://docutils.sourceforge.net/" /> +<title>Compiler Proof</title> +<link rel="stylesheet" href="alectryon.css" type="text/css" /> +<link rel="stylesheet" href="docutils_basic.css" type="text/css" /> +<link rel="stylesheet" href="tango_subtle.css" type="text/css" /> +<link rel="stylesheet" href="tango_subtle.min.css" type="text/css" /> +<script type="text/javascript" src="alectryon.js"></script> +<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/IBM-type/0.5.4/css/ibm-type.min.css" integrity="sha512-sky5cf9Ts6FY1kstGOBHSybfKqdHR41M0Ldb0BjNiv3ifltoQIsg0zIaQ+wwdwgQ0w9vKFW7Js50lxH9vqNSSw==" crossorigin="anonymous" /> +<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/firacode/5.2.0/fira_code.min.css" integrity="sha512-MbysAYimH1hH2xYzkkMHB6MqxBqfP0megxsCLknbYqHVwXTCg9IqHbk+ZP/vnhO8UEW6PaXAkKe2vQ+SWACxxA==" crossorigin="anonymous" /> +<link rel="stylesheet" href="../css/org.css" type="text/css" media="screen" /></head> +<body><header id="header" class="status"><div id="left-bar"><header><div class="logo"><a href="/vericert">Vericert</a></div><nav id="navbar"><span><a href="/vericert/documentation.html">Documentation</a></span><span><a href="/vericert/proof/toc.html">Proof</a></span></nav><p>Vericert is the first formally verified high-level synthesis tool.</p></<div id="toc"></div></div></header> +<div class="alectryon-root alectryon-floating"><div class="document" id="compiler-proof"> +<h1 class="title">Compiler Proof</h1> + +<div class="contents topic" id="table-of-contents"> +<p class="topic-title">Table of Contents</p> +<ul class="simple"> +<li><a class="reference internal" href="#imports" id="id1">Imports</a></li> +<li><a class="reference internal" href="#declarations" id="id2">Declarations</a><ul> +<li><a class="reference internal" href="#top-level-translation" id="id3">Top-level Translation</a></li> +</ul> +</li> +<li><a class="reference internal" href="#correctness-proof" id="id4">Correctness Proof</a><ul> +<li><a class="reference internal" href="#backward-simulation" id="id5">Backward Simulation</a></li> +</ul> +</li> +</ul> +</div> +<p>This is the top-level module of the correctness proof and proves the final backwards simulation correct.</p> +<div class="section" id="imports"> +<h1><a class="toc-backref" href="#id1">Imports</a></h1> +<p>We first need to import all of the modules that are used in the correctness proof, which includes all of the passes that are performed in Vericert and the CompCert front end.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> vericert <span class="kn">Require Import</span> HTLgenproof.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> compcert.common <span class="kn">Require Import</span> + Errors + Linking.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> compcert.lib <span class="kn">Require Import</span> + Coqlib.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> compcert.backend <span class="kn">Require</span> + Selection + RTL + RTLgen + Tailcall + Inlining + Renumber + Constprop + CSE + Deadcode + Unusedglob.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> compcert.cfrontend <span class="kn">Require</span> + Csyntax + SimplExpr + SimplLocals + Cshmgen + Cminorgen.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> compcert.driver <span class="kn">Require</span> + Compiler.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> vericert <span class="kn">Require</span> + Verilog + Veriloggen + Veriloggenproof + HTLgen + RTLBlock + RTLBlockgen + HTLSchedulegen.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> compcert <span class="kn">Require Import</span> Smallstep.</span></span></span></pre></div> +<div class="section" id="declarations"> +<h1><a class="toc-backref" href="#id2">Declarations</a></h1> +<p>We then need to declare the external OCaml functions used to print out intermediate steps in the compilation, such as <tt class="docutils literal">print_RTL</tt>, <tt class="docutils literal">print_HTL</tt> and <tt class="docutils literal">print_RTLBlock</tt>.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Parameter</span> <span class="nv">print_RTL</span>: Z -> RTL.program -> unit.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Parameter</span> <span class="nv">print_HTL</span>: HTL.program -> unit.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Parameter</span> <span class="nv">print_RTLBlock</span>: RTLBlock.program -> unit.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">print</span> {<span class="nv">A</span>: <span class="kt">Type</span>} (<span class="nv">printer</span>: A -> unit) (<span class="nv">prog</span>: A) : A := + <span class="kr">let</span> <span class="nv">unused</span> := printer prog <span class="kr">in</span> prog.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk0" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk0"><span class="highlight"><span class="kn">Lemma</span> <span class="nf">print_identity</span>: + <span class="kr">forall</span> (<span class="nv">A</span>: <span class="kt">Type</span>) (<span class="nv">printer</span>: A -> unit) (<span class="nv">prog</span>: A), + print printer prog = prog.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">A</span> : <span class="kt">Type</span>) (<span class="nv">printer</span> : A -> unit) (<span class="nv">prog</span> : A), +print printer prog = prog</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk1" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk1"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">A</span> : <span class="kt">Type</span>) (<span class="nv">printer</span> : A -> unit) (<span class="nv">prog</span> : A), +print printer prog = prog</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk2" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk2"><span class="highlight"><span class="nb">intros</span>; <span class="nb">unfold</span> print.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">A</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kt">Type</span></span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">printer</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A -> unit</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">prog</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">prog = prog</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">destruct</span> (printer prog); <span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span></span></pre><p>We also declare some new notation, which is also used in CompCert to combine the monadic results of each pass.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Notation</span> <span class="s2">"a @@@ b"</span> := + (Compiler.apply_partial _ _ a b) (<span class="kn">at level</span> <span class="mi">50</span>, <span class="kn">left associativity</span>).</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Notation</span> <span class="s2">"a @@ b"</span> := + (Compiler.apply_total _ _ a b) (<span class="kn">at level</span> <span class="mi">50</span>, <span class="kn">left associativity</span>).</span></span></span></pre><p>As printing is used in the translation but does not change the output, we need to prove that it has no effect so that it can be removed during the proof.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk3" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk3"><span class="highlight"><span class="kn">Lemma</span> <span class="nf">compose_print_identity</span>: + <span class="kr">forall</span> (<span class="nv">A</span>: <span class="kt">Type</span>) (<span class="nv">x</span>: res A) (<span class="nv">f</span>: A -> unit), + x @@ print f = x.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">A</span> : <span class="kt">Type</span>) (<span class="nv">x</span> : res A) (<span class="nv">f</span> : A -> unit), +x @@ print f = x</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk4" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk4"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">A</span> : <span class="kt">Type</span>) (<span class="nv">x</span> : res A) (<span class="nv">f</span> : A -> unit), +x @@ print f = x</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk5" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk5"><span class="highlight"><span class="nb">intros</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">A</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kt">Type</span></span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">x</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">res A</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">f</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A -> unit</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">x @@ print f = x</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk6" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk6"><span class="highlight"><span class="nb">destruct</span> x; <span class="nb">simpl</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">A</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kt">Type</span></span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">a</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">f</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A -> unit</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">OK (print f a) = OK a</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk7" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">A</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kt">Type</span></span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">e</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">errmsg</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">f</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A -> unit</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk7"><hr></label><div class="goal-conclusion"><span class="highlight">Error e = Error e</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk8" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk8"><span class="highlight"><span class="nb">rewrite</span> print_identity.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">A</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kt">Type</span></span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">a</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">f</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A -> unit</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">OK a = OK a</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk9" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">A</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kt">Type</span></span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">e</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">errmsg</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">f</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A -> unit</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk9"><hr></label><div class="goal-conclusion"><span class="highlight">Error e = Error e</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chka" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chka"><span class="highlight"><span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">A</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kt">Type</span></span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">e</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">errmsg</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">f</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">A -> unit</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Error e = Error e</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span></span></pre><p>Finally, some optimisation passes are only activated by a flag, which is handled by the following functions for partial and total passes.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">total_if</span> {<span class="nv">A</span>: <span class="kt">Type</span>} + (<span class="nv">flag</span>: unit -> bool) (<span class="nv">f</span>: A -> A) (<span class="nv">prog</span>: A) : A := + <span class="kr">if</span> flag tt <span class="kr">then</span> f prog <span class="kr">else</span> prog.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">partial_if</span> {<span class="nv">A</span>: <span class="kt">Type</span>} + (<span class="nv">flag</span>: unit -> bool) (<span class="nv">f</span>: A -> res A) (<span class="nv">prog</span>: A) : res A := + <span class="kr">if</span> flag tt <span class="kr">then</span> f prog <span class="kr">else</span> OK prog.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">time</span> {<span class="nv">A</span> <span class="nv">B</span>: <span class="kt">Type</span>} (<span class="nv">name</span>: string) (<span class="nv">f</span>: A -> B) : A -> B := f.</span></span></span></pre><div class="section" id="top-level-translation"> +<h2><a class="toc-backref" href="#id3">Top-level Translation</a></h2> +<p>An optimised transformation function from <tt class="docutils literal">RTL</tt> to <tt class="docutils literal">Verilog</tt> can then be defined, which applies the front end compiler optimisations of CompCert to the RTL that is generated and then performs the two Vericert passes from RTL to HTL and then from HTL to Verilog.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">transf_backend_opt</span> (<span class="nv">r</span> : RTL.program) : res Verilog.program := + OK r + @@@ Inlining.transf_program + @@ print (print_RTL <span class="mi">1</span>) + @@ Renumber.transf_program + @@ print (print_RTL <span class="mi">2</span>) + @@ total_if Compopts.optim_constprop (<span class="kp">time</span> <span class="s2">"Constant propagation"</span> Constprop.transf_program) + @@ print (print_RTL <span class="mi">3</span>) + @@ total_if Compopts.optim_constprop (<span class="kp">time</span> <span class="s2">"Renumbering"</span> Renumber.transf_program) + @@ print (print_RTL <span class="mi">4</span>) + @@@ partial_if Compopts.optim_CSE (<span class="kp">time</span> <span class="s2">"CSE"</span> CSE.transf_program) + @@ print (print_RTL <span class="mi">5</span>) + @@@ partial_if Compopts.optim_redundancy (<span class="kp">time</span> <span class="s2">"Redundancy elimination"</span> Deadcode.transf_program) + @@ print (print_RTL <span class="mi">6</span>) + @@@ <span class="kp">time</span> <span class="s2">"Unused globals"</span> Unusedglob.transform_program + @@ print (print_RTL <span class="mi">7</span>) + @@@ HTLgen.transl_program + @@ print print_HTL + @@ Veriloggen.transl_program.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">transf_backend</span> (<span class="nv">r</span> : RTL.program) : res Verilog.program := + OK r + @@@ Inlining.transf_program + @@ print (print_RTL <span class="mi">1</span>) + @@ Renumber.transf_program + @@ print (print_RTL <span class="mi">2</span>) + @@@ HTLgen.transl_program + @@ print print_HTL + @@ Veriloggen.transl_program.</span></span></span></pre><p>The transformation functions from RTL to Verilog are then added to the backend of the CompCert transformations from Clight to RTL.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">transf_hls</span> (<span class="nv">p</span> : Csyntax.program) : res Verilog.program := + OK p + @@@ SimplExpr.transl_program + @@@ SimplLocals.transf_program + @@@ Cshmgen.transl_program + @@@ Cminorgen.transl_program + @@@ Selection.sel_program + @@@ RTLgen.transl_program + @@ print (print_RTL <span class="mi">0</span>) + @@@ transf_backend.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">transf_hls_opt</span> (<span class="nv">p</span> : Csyntax.program) : res Verilog.program := + OK p + @@@ SimplExpr.transl_program + @@@ SimplLocals.transf_program + @@@ Cshmgen.transl_program + @@@ Cminorgen.transl_program + @@@ Selection.sel_program + @@@ RTLgen.transl_program + @@ print (print_RTL <span class="mi">0</span>) + @@@ transf_backend_opt.</span></span></span></pre></div> +</div> +<div class="section" id="correctness-proof"> +<h1><a class="toc-backref" href="#id4">Correctness Proof</a></h1> +<p>Finally, the top-level definition for all the passes is defined, which combines the <tt class="docutils literal">match_prog</tt> predicates of each translation pass from C until Verilog.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Local Open Scope</span> linking_scope.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">CompCert's_passes</span> := + mkpass SimplExprproof.match_prog + ::: mkpass SimplLocalsproof.match_prog + ::: mkpass Cshmgenproof.match_prog + ::: mkpass Cminorgenproof.match_prog + ::: mkpass Selectionproof.match_prog + ::: mkpass RTLgenproof.match_prog + ::: mkpass Inliningproof.match_prog + ::: mkpass Renumberproof.match_prog + ::: (@mkpass _ _ HTLgenproof.match_prog (HTLgenproof.TransfHTLLink HTLgen.transl_program)) + ::: mkpass Veriloggenproof.match_prog + ::: pass_nil _.</span></span></span></pre><p>These passes are then composed into a larger, top-level <tt class="docutils literal">match_prog</tt> predicate which matches a C program directly with a Verilog program.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">match_prog</span>: Csyntax.program -> Verilog.program -> <span class="kt">Prop</span> := + pass_match (compose_passes CompCert's_passes).</span></span></span></pre><p>We then need to prove that this predicate holds, assuming that the translation is performed using the <tt class="docutils literal">transf_hls</tt> function declared above.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chkb" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chkb"><span class="highlight"><span class="kn">Theorem</span> <span class="nf">transf_hls_match</span>: + <span class="kr">forall</span> <span class="nv">p</span> <span class="nv">tp</span>, + transf_hls p = OK tp -> + match_prog p tp.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +transf_hls p = OK tp -> match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chkc" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chkc"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +transf_hls p = OK tp -> match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chkd" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chkd"><span class="highlight"><span class="nb">intros</span> p tp T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">transf_hls p = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chke" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chke"><span class="highlight"><span class="nb">unfold</span> transf_hls <span class="kr">in</span> T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p @@@ SimplExpr.transl_program @@@ +SimplLocals.transf_program @@@ +Cshmgen.transl_program @@@ +Cminorgen.transl_program @@@ Selection.sel_program @@@ +RTLgen.transl_program @@ print (print_RTL <span class="mi">0</span>) @@@ +transf_backend = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chkf" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chkf"><span class="highlight"><span class="nb">simpl</span> <span class="kr">in</span> T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p @@@ +SimplLocals.transf_program @@@ +Cshmgen.transl_program @@@ +Cminorgen.transl_program @@@ Selection.sel_program @@@ +RTLgen.transl_program @@ print (print_RTL <span class="mi">0</span>) @@@ +transf_backend = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk10" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk10"><span class="highlight"><span class="nb">destruct</span> (SimplExpr.transl_program p) <span class="kr">as</span> [p1|e] <span class="nb">eqn</span>:P1; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 @@@ +Cshmgen.transl_program @@@ +Cminorgen.transl_program @@@ Selection.sel_program @@@ +RTLgen.transl_program @@ print (print_RTL <span class="mi">0</span>) @@@ +transf_backend = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk11" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk11"><span class="highlight"><span class="nb">destruct</span> (SimplLocals.transf_program p1) <span class="kr">as</span> [p2|e] <span class="nb">eqn</span>:P2; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 @@@ +Cminorgen.transl_program @@@ Selection.sel_program @@@ +RTLgen.transl_program @@ print (print_RTL <span class="mi">0</span>) @@@ +transf_backend = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk12" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk12"><span class="highlight"><span class="nb">destruct</span> (Cshmgen.transl_program p2) <span class="kr">as</span> [p3|e] <span class="nb">eqn</span>:P3; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 @@@ +Selection.sel_program @@@ RTLgen.transl_program @@ +print (print_RTL <span class="mi">0</span>) @@@ transf_backend = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk13" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk13"><span class="highlight"><span class="nb">destruct</span> (Cminorgen.transl_program p3) <span class="kr">as</span> [p4|e] <span class="nb">eqn</span>:P4; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 @@@ RTLgen.transl_program @@ +print (print_RTL <span class="mi">0</span>) @@@ transf_backend = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk14" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk14"><span class="highlight"><span class="nb">destruct</span> (Selection.sel_program p4) <span class="kr">as</span> [p5|e] <span class="nb">eqn</span>:P5; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 @@ print (print_RTL <span class="mi">0</span>) @@@ +transf_backend = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk15" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk15"><span class="highlight"><span class="nb">rewrite</span> ! compose_print_identity <span class="kr">in</span> T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 @@@ transf_backend = +OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk16" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk16"><span class="highlight"><span class="nb">destruct</span> (RTLgen.transl_program p5) <span class="kr">as</span> [p6|e] <span class="nb">eqn</span>:P6; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">transf_backend p6 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk17" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk17"><span class="highlight"><span class="nb">unfold</span> transf_backend <span class="kr">in</span> T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p6 @@@ Inlining.transf_program @@ +print (print_RTL <span class="mi">1</span>) @@ Renumber.transf_program @@ +print (print_RTL <span class="mi">2</span>) @@@ HTLgen.transl_program @@ +print print_HTL @@ Veriloggen.transl_program = +OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk18" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk18"><span class="highlight"><span class="nb">simpl</span> <span class="kr">in</span> T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 @@ print (print_RTL <span class="mi">1</span>) @@ +Renumber.transf_program @@ print (print_RTL <span class="mi">2</span>) @@@ +HTLgen.transl_program @@ print print_HTL @@ +Veriloggen.transl_program = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk19" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk19"><span class="highlight"><span class="nb">rewrite</span> ! compose_print_identity <span class="kr">in</span> T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 @@ +Renumber.transf_program @@@ HTLgen.transl_program @@ +Veriloggen.transl_program = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk1a" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk1a"><span class="highlight"><span class="nb">destruct</span> (Inlining.transf_program p6) <span class="kr">as</span> [p7|e] <span class="nb">eqn</span>:P7; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program (Renumber.transf_program p7) @@ +Veriloggen.transl_program = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk1b" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk1b"><span class="highlight"><span class="nb">set</span> (p8 := Renumber.transf_program p7) <span class="kr">in</span> *.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 @@ +Veriloggen.transl_program = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk1c" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk1c"><span class="highlight"><span class="nb">destruct</span> (HTLgen.transl_program p8) <span class="kr">as</span> [p9|e] <span class="nb">eqn</span>:P9; <span class="nb">simpl</span> <span class="kr">in</span> T; <span class="kp">try</span> <span class="bp">discriminate</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK (Veriloggen.transl_program p9) = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk1d" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk1d"><span class="highlight"><span class="nb">set</span> (p10 := Veriloggen.transl_program p9) <span class="kr">in</span> *.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk1e" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk1e"><span class="highlight"><span class="nb">unfold</span> match_prog; <span class="nb">simpl</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Clight.program, + SimplExprproof.match_prog p p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : Clight.program, + SimplLocalsproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : Csharpminor.program, + Cshmgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : Cminor.program, + Cminorgenproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : CminorSel.program, + Selectionproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : RTL.program, + RTLgenproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : RTL.program, + Inliningproof.match_prog p7 p8 /\ + (<span class="kr">exists</span> <span class="nv">p9</span> : RTL.program, + Renumberproof.match_prog p8 p9 /\ + (<span class="kr">exists</span> <span class="nv">p10</span> : HTL.program, + HTLgenproof.match_prog p9 + p10 /\ (...)))))))))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk1f" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk1f"><span class="highlight"><span class="kr">exists</span> <span class="nv">p1</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">SimplExprproof.match_prog p p1</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk20" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk20"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Clight.program, + SimplLocalsproof.match_prog p1 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : Csharpminor.program, + Cshmgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : Cminor.program, + Cminorgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : CminorSel.program, + Selectionproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : RTL.program, + RTLgenproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : RTL.program, + Inliningproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : RTL.program, + Renumberproof.match_prog p7 p8 /\ + (<span class="kr">exists</span> <span class="nv">p9</span> : HTL.program, + HTLgenproof.match_prog p8 p9 /\ + (<span class="kr">exists</span> <span class="nv">p10</span> : Verilog.program, + Veriloggenproof.match_prog + p9 p10 /\ p10 = tp))))))))</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk21" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk21"><span class="highlight"><span class="nb">apply</span> SimplExprproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Clight.program, + SimplLocalsproof.match_prog p1 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : Csharpminor.program, + Cshmgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : Cminor.program, + Cminorgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : CminorSel.program, + Selectionproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : RTL.program, + RTLgenproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : RTL.program, + Inliningproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : RTL.program, + Renumberproof.match_prog p7 p8 /\ + (<span class="kr">exists</span> <span class="nv">p9</span> : HTL.program, + HTLgenproof.match_prog p8 p9 /\ + (<span class="kr">exists</span> <span class="nv">p10</span> : Verilog.program, + Veriloggenproof.match_prog + p9 p10 /\ p10 = tp))))))))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk22" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk22"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">SimplLocalsproof.match_prog p1 p2</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk23" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk23"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p3</span> : Csharpminor.program, + Cshmgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p2</span> : Cminor.program, + Cminorgenproof.match_prog p3 p2 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : CminorSel.program, + Selectionproof.match_prog p2 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : RTL.program, + RTLgenproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : RTL.program, + Inliningproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : RTL.program, + Renumberproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : HTL.program, + HTLgenproof.match_prog p7 p8 /\ + (<span class="kr">exists</span> <span class="nv">p9</span> : Verilog.program, + Veriloggenproof.match_prog p8 + p9 /\ p9 = tp)))))))</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk24" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk24"><span class="highlight"><span class="nb">apply</span> SimplLocalsproof.match_transf_program; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p3</span> : Csharpminor.program, + Cshmgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p2</span> : Cminor.program, + Cminorgenproof.match_prog p3 p2 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : CminorSel.program, + Selectionproof.match_prog p2 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : RTL.program, + RTLgenproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : RTL.program, + Inliningproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : RTL.program, + Renumberproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : HTL.program, + HTLgenproof.match_prog p7 p8 /\ + (<span class="kr">exists</span> <span class="nv">p9</span> : Verilog.program, + Veriloggenproof.match_prog p8 + p9 /\ p9 = tp)))))))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk25" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk25"><span class="highlight"><span class="kr">exists</span> <span class="nv">p3</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Cshmgenproof.match_prog p2 p3</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk26" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk26"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Cminor.program, + Cminorgenproof.match_prog p3 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : CminorSel.program, + Selectionproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : RTL.program, + RTLgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : RTL.program, + Inliningproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : RTL.program, + Renumberproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : HTL.program, + HTLgenproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : Verilog.program, + Veriloggenproof.match_prog p7 p8 /\ + p8 = tp))))))</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk27" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk27"><span class="highlight"><span class="nb">apply</span> Cshmgenproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Cminor.program, + Cminorgenproof.match_prog p3 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : CminorSel.program, + Selectionproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : RTL.program, + RTLgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : RTL.program, + Inliningproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : RTL.program, + Renumberproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : HTL.program, + HTLgenproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : Verilog.program, + Veriloggenproof.match_prog p7 p8 /\ + p8 = tp))))))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk28" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk28"><span class="highlight"><span class="kr">exists</span> <span class="nv">p4</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk29" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk29"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : CminorSel.program, + Selectionproof.match_prog p4 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : RTL.program, + RTLgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : RTL.program, + Inliningproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : RTL.program, + Renumberproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : HTL.program, + HTLgenproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : Verilog.program, + Veriloggenproof.match_prog p6 p7 /\ + p7 = tp)))))</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk2a" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk2a"><span class="highlight"><span class="nb">apply</span> Cminorgenproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : CminorSel.program, + Selectionproof.match_prog p4 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : RTL.program, + RTLgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : RTL.program, + Inliningproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : RTL.program, + Renumberproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : HTL.program, + HTLgenproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : Verilog.program, + Veriloggenproof.match_prog p6 p7 /\ + p7 = tp)))))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk2b" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk2b"><span class="highlight"><span class="kr">exists</span> <span class="nv">p5</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Selectionproof.match_prog p4 p5</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk2c" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk2c"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : RTL.program, + RTLgenproof.match_prog p5 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : RTL.program, + Inliningproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : RTL.program, + Renumberproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : HTL.program, + HTLgenproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : Verilog.program, + Veriloggenproof.match_prog p5 p6 /\ + p6 = tp))))</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk2d" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk2d"><span class="highlight"><span class="nb">apply</span> Selectionproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : RTL.program, + RTLgenproof.match_prog p5 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : RTL.program, + Inliningproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : RTL.program, + Renumberproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : HTL.program, + HTLgenproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : Verilog.program, + Veriloggenproof.match_prog p5 p6 /\ + p6 = tp))))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk2e" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk2e"><span class="highlight"><span class="kr">exists</span> <span class="nv">p6</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">RTLgenproof.match_prog p5 p6</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk2f" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk2f"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : RTL.program, + Inliningproof.match_prog p6 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : RTL.program, + Renumberproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : HTL.program, + HTLgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : Verilog.program, + Veriloggenproof.match_prog p4 p5 /\ p5 = tp)))</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk30" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk30"><span class="highlight"><span class="nb">apply</span> RTLgenproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : RTL.program, + Inliningproof.match_prog p6 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : RTL.program, + Renumberproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : HTL.program, + HTLgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : Verilog.program, + Veriloggenproof.match_prog p4 p5 /\ p5 = tp)))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk31" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk31"><span class="highlight"><span class="kr">exists</span> <span class="nv">p7</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Inliningproof.match_prog p6 p7</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk32" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk32"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : RTL.program, + Renumberproof.match_prog p7 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : HTL.program, + HTLgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : Verilog.program, + Veriloggenproof.match_prog p3 p4 /\ p4 = tp))</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk33" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk33"><span class="highlight"><span class="nb">apply</span> Inliningproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : RTL.program, + Renumberproof.match_prog p7 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : HTL.program, + HTLgenproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : Verilog.program, + Veriloggenproof.match_prog p3 p4 /\ p4 = tp))</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk34" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk34"><span class="highlight"><span class="kr">exists</span> <span class="nv">p8</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Renumberproof.match_prog p7 p8</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk35" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk35"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : HTL.program, + HTLgenproof.match_prog p8 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : Verilog.program, + Veriloggenproof.match_prog p2 p3 /\ p3 = tp)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk36" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk36"><span class="highlight"><span class="nb">apply</span> Renumberproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : HTL.program, + HTLgenproof.match_prog p8 p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : Verilog.program, + Veriloggenproof.match_prog p2 p3 /\ p3 = tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk37" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk37"><span class="highlight"><span class="kr">exists</span> <span class="nv">p9</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">HTLgenproof.match_prog p8 p9</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk38" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk38"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Verilog.program, + Veriloggenproof.match_prog p9 p2 /\ p2 = tp</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk39" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk39"><span class="highlight"><span class="nb">apply</span> HTLgenproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Verilog.program, + Veriloggenproof.match_prog p9 p2 /\ p2 = tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk3a" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk3a"><span class="highlight"><span class="kr">exists</span> <span class="nv">p10</span>; <span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk3b" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk3b"><hr></label><div class="goal-conclusion"><span class="highlight">p10 = tp</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk3c" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk3c"><span class="highlight"><span class="nb">apply</span> Veriloggenproof.transf_program_match; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">T</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">OK p10 = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">p10 = tp</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk3d" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk3d"><span class="highlight">inv T.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExpr.transl_program p = OK p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocals.transf_program p1 = OK p2</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgen.transl_program p2 = OK p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgen.transl_program p3 = OK p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selection.sel_program p4 = OK p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgen.transl_program p5 = OK p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inlining.transf_program p6 = OK p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Renumber.transf_program p7</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgen.transl_program p8 = OK p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-body-block"><span class="hyp-punct">:=</span><span class="hyp-body"><span class="highlight">Veriloggen.transl_program p9</span></span></span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">p10 = p10</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="bp">reflexivity</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk3e" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk3e"><span class="highlight"><span class="kn">Remark</span> <span class="nf">forward_simulation_identity</span>: + <span class="kr">forall</span> <span class="nv">sem</span>, forward_simulation sem sem.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> <span class="nv">sem</span> : semantics, forward_simulation sem sem</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk3f" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk3f"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> <span class="nv">sem</span> : semantics, forward_simulation sem sem</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk40" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk40"><span class="highlight"><span class="nb">intros</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation sem sem</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk41" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk41"><span class="highlight"><span class="nb">apply</span> forward_simulation_step <span class="kr">with</span> (<span class="kr">fun</span> <span class="nv">s1</span> <span class="nv">s2</span> => s2 = s1); <span class="nb">intros</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">id</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">AST.<span class="kn">ident</span></span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Globalenvs.Senv.public_symbol (symbolenv sem) id = +Globalenvs.Senv.public_symbol (symbolenv sem) id</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk42" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">initial_state sem s1</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk42"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">s2</span> : state sem, initial_state sem s2 /\ s2 = s1</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk43" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1, s2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">r</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Integers.Int.int</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">s2 = s1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">final_state sem s1 r</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk43"><hr></label><div class="goal-conclusion"><span class="highlight">final_state sem s2 r</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk44" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">t</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Events.trace</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1'</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Step sem s1 t s1'</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">s2 = s1</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk44"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">s2'</span> : state sem, Step sem s2 t s2' /\ s2' = s1'</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk45" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk45"><span class="highlight">-</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">id</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">AST.<span class="kn">ident</span></span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">Globalenvs.Senv.public_symbol (symbolenv sem) id = +Globalenvs.Senv.public_symbol (symbolenv sem) id</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk46" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk46"><span class="highlight">-</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">initial_state sem s1</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">s2</span> : state sem, initial_state sem s2 /\ s2 = s1</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kr">exists</span> <span class="nv">s1</span>; <span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk47" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk47"><span class="highlight">-</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1, s2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">r</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Integers.Int.int</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">s2 = s1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">final_state sem s1 r</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">final_state sem s2 r</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">subst</span> s2; <span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk48" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk48"><span class="highlight">-</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">t</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Events.trace</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1'</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Step sem s1 t s1'</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">s2 = s1</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">s2'</span> : state sem, Step sem s2 t s2' /\ s2' = s1'</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk49" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk49"><span class="highlight"><span class="nb">subst</span> s2.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">sem</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">semantics</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">t</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Events.trace</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">s1'</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">state sem</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Step sem s1 t s1'</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">s2'</span> : state sem, Step sem s1 t s2' /\ s2' = s1'</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kr">exists</span> <span class="nv">s1'</span>; <span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk4a" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk4a"><span class="highlight"><span class="kn">Theorem</span> <span class="nf">cstrategy_semantic_preservation</span>: + <span class="kr">forall</span> <span class="nv">p</span> <span class="nv">tp</span>, + match_prog p tp -> + forward_simulation (Cstrategy.semantics p) (Verilog.semantics tp) + /\ backward_simulation (atomic (Cstrategy.semantics p)) (Verilog.semantics tp).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +match_prog p tp -> +forward_simulation (Cstrategy.semantics p) + (Verilog.semantics tp) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk4b" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk4b"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +match_prog p tp -> +forward_simulation (Cstrategy.semantics p) + (Verilog.semantics tp) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk4c" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk4c"><span class="highlight"><span class="nb">intros</span> p tp M.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics tp) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk4d" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk4d"><span class="highlight"><span class="nb">unfold</span> match_prog, pass_match <span class="kr">in</span> M; <span class="nb">simpl</span> <span class="kr">in</span> M.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Clight.program, + SimplExprproof.match_prog p p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : Clight.program, + SimplLocalsproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : Csharpminor.program, + Cshmgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : Cminor.program, + Cminorgenproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : CminorSel.program, + Selectionproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : RTL.program, + RTLgenproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : RTL.program, + Inliningproof.match_prog p7 p8 /\ + (<span class="kr">exists</span> <span class="nv">p9</span> : RTL.program, + Renumberproof.match_prog p8 + p9 /\ + (<span class="kr">exists</span> <span class="nv">p10</span> : HTL.program, + HTLgenproof.match_prog + p9 p10 /\ (...)))))))))</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics tp) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk4e" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk4e"><span class="highlight"><span class="kn">Ltac</span> <span class="nf">DestructM</span> := + <span class="kr">match goal with</span> + [ H: <span class="kr">exists</span> <span class="nv">p</span>, _ /\ _ |- _ ] => + <span class="kr">let</span> <span class="nv">p</span> := <span class="kp">fresh</span> <span class="s2">"p"</span> <span class="kr">in</span> <span class="kr">let</span> <span class="nv">M</span> := <span class="kp">fresh</span> <span class="s2">"M"</span> <span class="kr">in</span> <span class="kr">let</span> <span class="nv">MM</span> := <span class="kp">fresh</span> <span class="s2">"MM"</span> <span class="kr">in</span> + <span class="nb">destruct</span> H <span class="kr">as</span> (p & M & MM); <span class="nb">clear</span> H + <span class="kr">end</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kr">exists</span> <span class="nv">p2</span> : Clight.program, + SimplExprproof.match_prog p p2 /\ + (<span class="kr">exists</span> <span class="nv">p3</span> : Clight.program, + SimplLocalsproof.match_prog p2 p3 /\ + (<span class="kr">exists</span> <span class="nv">p4</span> : Csharpminor.program, + Cshmgenproof.match_prog p3 p4 /\ + (<span class="kr">exists</span> <span class="nv">p5</span> : Cminor.program, + Cminorgenproof.match_prog p4 p5 /\ + (<span class="kr">exists</span> <span class="nv">p6</span> : CminorSel.program, + Selectionproof.match_prog p5 p6 /\ + (<span class="kr">exists</span> <span class="nv">p7</span> : RTL.program, + RTLgenproof.match_prog p6 p7 /\ + (<span class="kr">exists</span> <span class="nv">p8</span> : RTL.program, + Inliningproof.match_prog p7 p8 /\ + (<span class="kr">exists</span> <span class="nv">p9</span> : RTL.program, + Renumberproof.match_prog p8 + p9 /\ + (<span class="kr">exists</span> <span class="nv">p10</span> : HTL.program, + HTLgenproof.match_prog + p9 p10 /\ (...)))))))))</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics tp) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk4f" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk4f"><span class="highlight"><span class="kp">repeat</span> DestructM.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">MM0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">p10 = tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics tp) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk50" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk50"><span class="highlight"><span class="nb">subst</span> tp.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk51" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk51"><span class="highlight"><span class="nb">assert</span> (F: forward_simulation (Cstrategy.semantics p) (Verilog.semantics p10)).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk52" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk52"><hr></label><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk53" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk53"><span class="highlight">{</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk54" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk54"><span class="highlight"><span class="nb">eapply</span> SimplExprproof.transl_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Clight.semantics1 p0) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk55" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk55"><span class="highlight"><span class="nb">eapply</span> SimplLocalsproof.transf_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Clight.semantics2 p1) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk56" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk56"><span class="highlight"><span class="nb">eapply</span> Cshmgenproof.transl_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Csharpminor.semantics p3) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk57" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk57"><span class="highlight"><span class="nb">eapply</span> Cminorgenproof.transl_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cminor.semantics p4) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk58" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk58"><span class="highlight"><span class="nb">eapply</span> Selectionproof.transf_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (CminorSel.semantics p5) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk59" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk59"><span class="highlight"><span class="nb">eapply</span> RTLgenproof.transf_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (RTL.semantics p6) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk5a" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk5a"><span class="highlight"><span class="nb">eapply</span> Inliningproof.transf_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (RTL.semantics p7) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk5b" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk5b"><span class="highlight"><span class="nb">eapply</span> Renumberproof.transf_program_correct; <span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (RTL.semantics p8) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> compose_forward_simulations.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> HTLgenproof.transf_program_correct.</span></span><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk5c" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk5c"><span class="highlight"><span class="bp">eassumption</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (HTL.semantics p9) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> Veriloggenproof.transf_program_correct; <span class="bp">eassumption</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk5d" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk5d"><span class="highlight">}</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10) /\ +backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk5e" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk5e"><span class="highlight"><span class="nb">split</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk5f" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk5f"><hr></label><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk60" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk60"><span class="highlight"><span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk61" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk61"><span class="highlight"><span class="nb">apply</span> forward_to_backward_simulation.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics p10)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk62" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk62"><hr></label><div class="goal-conclusion"><span class="highlight">receptive (atomic (Cstrategy.semantics p))</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk63" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk63"><hr></label><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk64" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk64"><span class="highlight"><span class="nb">apply</span> factor_forward_simulation.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk65" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk65"><hr></label><div class="goal-conclusion"><span class="highlight">single_events (Verilog.semantics p10)</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk66" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk66"><hr></label><div class="goal-conclusion"><span class="highlight">receptive (atomic (Cstrategy.semantics p))</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk67" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk67"><hr></label><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk68" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk68"><span class="highlight"><span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">single_events (Verilog.semantics p10)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk69" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk69"><hr></label><div class="goal-conclusion"><span class="highlight">receptive (atomic (Cstrategy.semantics p))</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk6a" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk6a"><hr></label><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk6b" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk6b"><span class="highlight"><span class="nb">eapply</span> sd_traces.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk6c" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk6c"><hr></label><div class="goal-conclusion"><span class="highlight">receptive (atomic (Cstrategy.semantics p))</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk6d" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk6d"><hr></label><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk6e" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk6e"><span class="highlight"><span class="nb">eapply</span> Verilog.semantics_determinate.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">receptive (atomic (Cstrategy.semantics p))</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk6f" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk6f"><hr></label><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk70" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk70"><span class="highlight"><span class="nb">apply</span> atomic_receptive.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">strongly_receptive (Cstrategy.semantics p)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk71" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk71"><hr></label><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk72" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk72"><span class="highlight"><span class="nb">apply</span> Cstrategy.semantics_strongly_receptive.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplExprproof.match_prog p p0</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Clight.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">SimplLocalsproof.match_prog p0 p1</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csharpminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cshmgenproof.match_prog p1 p3</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminor.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Cminorgenproof.match_prog p3 p4</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">CminorSel.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Selectionproof.match_prog p4 p5</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M4</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTLgenproof.match_prog p5 p6</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M5</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Inliningproof.match_prog p6 p7</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">RTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M6</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Renumberproof.match_prog p7 p8</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p9</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTL.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M7</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">HTLgenproof.match_prog p8 p9</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">p10</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">M8</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Veriloggenproof.match_prog p9 p10</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">F</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">forward_simulation (Cstrategy.semantics p) + (Verilog.semantics p10)</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">determinate (Verilog.semantics p10)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">apply</span> Verilog.semantics_determinate.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span></span></pre><div class="section" id="backward-simulation"> +<h2><a class="toc-backref" href="#id5">Backward Simulation</a></h2> +<p>The following theorem is a <em>backward simulation</em> between the C and Verilog, which proves the semantics preservation of the translation. We can assume that the C and Verilog programs match, as we have proven previously in <tt class="docutils literal">transf_hls_match</tt> that our translation implies that the <tt class="docutils literal">match_prog</tt> predicate will hold.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk73" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk73"><span class="highlight"><span class="kn">Theorem</span> <span class="nf">c_semantic_preservation</span>: + <span class="kr">forall</span> <span class="nv">p</span> <span class="nv">tp</span>, + match_prog p tp -> + backward_simulation (Csem.semantics p) (Verilog.semantics tp).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +match_prog p tp -> +backward_simulation (Csem.semantics p) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk74" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk74"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +match_prog p tp -> +backward_simulation (Csem.semantics p) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk75" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk75"><span class="highlight"><span class="nb">intros</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">backward_simulation (Csem.semantics p) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk76" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk76"><span class="highlight"><span class="nb">apply</span> compose_backward_simulation <span class="kr">with</span> (atomic (Cstrategy.semantics p)).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">single_events (Verilog.semantics tp)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk77" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk77"><hr></label><div class="goal-conclusion"><span class="highlight">backward_simulation (Csem.semantics p) + (atomic (Cstrategy.semantics p))</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk78" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk78"><hr></label><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk79" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk79"><span class="highlight"><span class="nb">eapply</span> sd_traces; <span class="nb">eapply</span> Verilog.semantics_determinate.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">backward_simulation (Csem.semantics p) + (atomic (Cstrategy.semantics p))</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk7a" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk7a"><hr></label><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk7b" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk7b"><span class="highlight"><span class="nb">apply</span> factor_backward_simulation.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">backward_simulation (Csem.semantics p) + (Cstrategy.semantics p)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk7c" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk7c"><hr></label><div class="goal-conclusion"><span class="highlight">single_events (Csem.semantics p)</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk7d" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk7d"><hr></label><div class="goal-conclusion"><span class="highlight">well_behaved_traces (Cstrategy.semantics p)</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk7e" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk7e"><hr></label><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk7f" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk7f"><span class="highlight"><span class="nb">apply</span> Cstrategy.strategy_simulation.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">single_events (Csem.semantics p)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk80" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk80"><hr></label><div class="goal-conclusion"><span class="highlight">well_behaved_traces (Cstrategy.semantics p)</span></div></blockquote><input class="coq-extra-goal-toggle" id="compiler-v-chk81" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk81"><hr></label><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk82" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk82"><span class="highlight"><span class="nb">apply</span> Csem.semantics_single_events.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">well_behaved_traces (Cstrategy.semantics p)</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk83" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk83"><hr></label><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk84" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk84"><span class="highlight"><span class="nb">eapply</span> ssr_well_behaved; <span class="nb">eapply</span> Cstrategy.semantics_strongly_receptive.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog p tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">backward_simulation (atomic (Cstrategy.semantics p)) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="bp">exact</span> (proj2 (cstrategy_semantic_preservation _ _ H)).</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span></span></pre><p>We can then use <tt class="docutils literal">transf_hls_match</tt> to prove the backward simulation where the assumption is that the translation is performed using the <tt class="docutils literal">transf_hls</tt> function and that it succeeds.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk85" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk85"><span class="highlight"><span class="kn">Theorem</span> <span class="nf">transf_c_program_correct</span>: + <span class="kr">forall</span> <span class="nv">p</span> <span class="nv">tp</span>, + transf_hls p = OK tp -> + backward_simulation (Csem.semantics p) (Verilog.semantics tp).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +transf_hls p = OK tp -> +backward_simulation (Csem.semantics p) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk86" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk86"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">p</span> : Csyntax.program) (<span class="nv">tp</span> : Verilog.program), +transf_hls p = OK tp -> +backward_simulation (Csem.semantics p) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk87" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk87"><span class="highlight"><span class="nb">intros</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">transf_hls p = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">backward_simulation (Csem.semantics p) + (Verilog.semantics tp)</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk88" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk88"><span class="highlight"><span class="nb">apply</span> c_semantic_preservation.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">p</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">tp</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">transf_hls p = OK tp</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog p tp</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">apply</span> transf_hls_match; <span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span></span></pre><p>The final theorem of the semantic preservation of the translation of separate translation units can also be proven correct, however, this is only because the translation fails if more than one translation unit is passed to Vericert at the moment.</p> +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk89" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk89"><span class="highlight"><span class="kn">Theorem</span> <span class="nf">separate_transf_c_program_correct</span>: + <span class="kr">forall</span> <span class="nv">c_units</span> <span class="nv">verilog_units</span> <span class="nv">c_program</span>, + nlist_forall2 (<span class="kr">fun</span> <span class="nv">cu</span> <span class="nv">tcu</span> => transf_hls cu = OK tcu) c_units verilog_units -> + link_list c_units = Some c_program -> + <span class="kr">exists</span> <span class="nv">verilog_program</span>, + link_list verilog_units = Some verilog_program + /\ backward_simulation (Csem.semantics c_program) (Verilog.semantics verilog_program).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">c_units</span> : nlist Csyntax.program) + (<span class="nv">verilog_units</span> : nlist Verilog.program) + (<span class="nv">c_program</span> : Csyntax.program), +nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) (<span class="nv">tcu</span> : Verilog.program) + => transf_hls cu = OK tcu) c_units verilog_units -> +link_list c_units = Some c_program -> +<span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk8a" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk8a"><span class="highlight"><span class="kn">Proof</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">c_units</span> : nlist Csyntax.program) + (<span class="nv">verilog_units</span> : nlist Verilog.program) + (<span class="nv">c_program</span> : Csyntax.program), +nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) (<span class="nv">tcu</span> : Verilog.program) + => transf_hls cu = OK tcu) c_units verilog_units -> +link_list c_units = Some c_program -> +<span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk8b" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk8b"><span class="highlight"><span class="nb">intros</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk8c" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk8c"><span class="highlight"><span class="nb">assert</span> (nlist_forall2 match_prog c_units verilog_units).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk8d" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk8d"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk8e" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk8e"><span class="highlight">{</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> nlist_forall2_imply.</span></span><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk8f" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk8f"><span class="highlight"><span class="nb">eauto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">forall</span> (<span class="nv">v1</span> : Csyntax.program) (<span class="nv">v2</span> : Verilog.program), +nIn v1 c_units -> +nIn v2 verilog_units -> +(<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) v1 v2 -> +match_prog v1 v2</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk90" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk90"><span class="highlight"><span class="nb">simpl</span>; <span class="nb">intros</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">v1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">v2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nIn v1 c_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nIn v2 verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H3</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">transf_hls v1 = OK v2</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">match_prog v1 v2</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">apply</span> transf_hls_match; <span class="nb">auto</span>.</span></span><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk91" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk91"><span class="highlight">}</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk92" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk92"><span class="highlight"><span class="nb">assert</span> (<span class="kr">exists</span> <span class="nv">verilog_program</span>, link_list verilog_units = Some verilog_program + /\ match_prog c_program verilog_program).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + match_prog c_program verilog_program</span></div></blockquote><div class="coq-extra-goals"><input class="coq-extra-goal-toggle" id="compiler-v-chk93" style="display: none" type="checkbox"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + match_prog c_program verilog_program</span></span></span></span></div></div><label class="goal-separator coq-extra-goal-label" for="compiler-v-chk93"><hr></label><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk94" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk94"><span class="highlight">{</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + match_prog c_program verilog_program</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">eapply</span> link_list_compose_passes; <span class="nb">eauto</span>.</span></span><span class="coq-wsp"> </span></span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk95" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk95"><span class="highlight">}</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H2</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + match_prog c_program verilog_program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk96" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk96"><span class="highlight"><span class="nb">destruct</span> H2 <span class="kr">as</span> (verilog_program & P & Q).</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list verilog_units = Some verilog_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">Q</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog c_program verilog_program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span> : Verilog.program, + link_list verilog_units = Some verilog_program /\ + backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></small><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><input class="coq-toggle" id="compiler-v-chk97" style="display: none" type="checkbox"><label class="coq-input" for="compiler-v-chk97"><span class="highlight"><span class="kr">exists</span> <span class="nv">verilog_program</span>; <span class="nb">split</span>; <span class="nb">auto</span>.</span></label><small class="coq-output"><div class="coq-output-sticky-wrapper"><div class="coq-goals"><blockquote class="coq-goal"><div class="goal-hyps"><div class="goal-hyp"><span class="hyp-names">c_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_units</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">c_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Csyntax.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 + (<span class="kr">fun</span> (<span class="nv">cu</span> : Csyntax.program) + (<span class="nv">tcu</span> : Verilog.program) => + transf_hls cu = OK tcu) c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H0</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list c_units = Some c_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">H1</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">nlist_forall2 match_prog c_units verilog_units</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">verilog_program</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">Verilog.program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">P</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">link_list verilog_units = Some verilog_program</span></span></span></span></div><div class="goal-hyp"><span class="hyp-names">Q</span><span><span class="hyp-type-block"><span class="hyp-punct">:</span><span class="hyp-type"><span class="highlight">match_prog c_program verilog_program</span></span></span></span></div></div><span class="goal-separator"><hr></span><div class="goal-conclusion"><span class="highlight">backward_simulation (Csem.semantics c_program) + (Verilog.semantics verilog_program)</span></div></blockquote></div></div></small><span class="coq-wsp"> </span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="nb">apply</span> c_semantic_preservation; <span class="nb">auto</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Qed</span>.</span></span></span></pre></div> +</div> +</div> +</div> +</body> +</html> |