<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>40</sub></font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>39</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>41</sub></font> =  <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>39</sub></font>;<br/>
<a NAME="E1:69"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>39</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T10" target="_self">Th10</a></i>;<br/>
<i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>39</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T9">SCMFSA6C:9</a></i>
<br/>.= 
<font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_2"/>
( <font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_1"><b>suppose </b></a><a NAME="E1:69_2_1"/>
<font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>,<font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scm_halt.html#T54">SCM_HALT:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>39</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T7">SCMFSA6C:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:69"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_2"><b>suppose </b></a><a NAME="E1:69_2_2"/>
<font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>,<font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scm_halt.html#T54">SCM_HALT:54</a></i>
<br/>.= 
<font color="Maroon">c<sub>39</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmbsort.html#T12" target="_self">Th12</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

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