<?xml version="1.0"?>
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<b>let </b><font color="Maroon">a</font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>



<b>assume </b><a NAME="E1:61"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <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> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 ;<br/>

<b>set </b><font color="Maroon">s1</font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <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 class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">s2</font> =  <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <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 class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/>
<i><font color="Green">E41</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <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 class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>
<i><font color="Green">E43</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"><a href="scmfsa_2.html#K9">AddTo</a> <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 class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <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 class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T9">SCMFSA6C:9</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:61_3"/>
( <font color="Maroon">s</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">4 <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">s</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">4 <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="61_3_1"><b>suppose </b></a><a NAME="E1:61_3_1"/>
<font color="Maroon">s</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">4 <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">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <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 class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<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"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <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">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T6">SCMFSA6C:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_3_2"><b>suppose </b></a><a NAME="E1:61_3_2"/>
<font color="Maroon">s</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">4 <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><a NAME="E2:61_3_2"/>
<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">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <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 class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="scm_halt.html#T54">SCM_HALT:54</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
