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<b>let </b><font color="Maroon">s1</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">s2</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">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">I</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green">E34</font></i>: 
 <a href="scmfsa9a.html#R3" target="_self">ProperBodyWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s1</font>
 ;<br/>

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="scmfsa9a.html#D4" target="_self">SCMFSA9A:def 4</a><br/>

<b>assume </b><a NAME="E3:49"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E4:49"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:49"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="scmfsa9a.html#T6" target="_self">Th6</a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>;<br/>
<a NAME="E6:49"/><b>then </b>
( <font color="Maroon">I</font> <a href="scmfsa7b.html#R5">is_closed_on</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> &amp; <font color="Maroon">I</font> <a href="scmfsa7b.html#R6">is_halting_on</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:49"/>
( <font color="Maroon">I</font> <a href="scmfsa7b.html#R5">is_closed_on</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> &amp; <font color="Maroon">I</font> <a href="scmfsa7b.html#R6">is_halting_on</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa8b.html#T8">SCMFSA8B:8</a></i>;<br/>


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