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<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>let </b><font color="Maroon">I</font> be  <a href="scmfsa6b.html#V2">parahalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>, <font color="Maroon">J</font> be  <a href="scmfsa6b.html#V2">parahalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><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/>





<a NAME="E1:38"/>
 <a href="scmfsa8b.html#K2" target="_self">if&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">I</font> is <a href="scmfsa6b.html#V2">parahalting</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:38"/>
 <a href="scmfsa8b.html#K3" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> is <a href="scmfsa6b.html#V2">parahalting</a>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1"><i><font color="Green">Lemma26</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:38_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><a NAME="E2:38_1"/>
( <font color="Maroon">I</font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font> &amp; <font color="Maroon">I</font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font> )
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T24">SCMFSA7B:24</a>, <a class="ref" href="scmfsa7b.html#T25">SCMFSA7B:25</a></i>;<br/><b>hence </b><a NAME="E3:38_1"/>
 <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K3" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>,<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">I</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <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="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 7</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8b.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa8b.html#T1" target="_self">Th1</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:38_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><a NAME="E2:38_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">J</font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font> &amp; <font color="Maroon">J</font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font> )
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T24">SCMFSA7B:24</a>, <a class="ref" href="scmfsa7b.html#T25">SCMFSA7B:25</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_2_1"/>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_1_1"><b>suppose </b></a><a NAME="E1:38_2_1_1"/>
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:38_2_1_1"/>
 <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K3" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>,<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <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="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 7</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8b.html#T3" target="_self">Th3</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_1_2"><b>suppose </b></a><a NAME="E1:38_2_1_2"/>
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:38_2_1_2"/>
 <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K3" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>,<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <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="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 7</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8b.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa8b.html#T3" target="_self">Th3</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>


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