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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">b</font> be    <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>set </b><font color="Maroon">a</font> = <font color="Maroon">b</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green">E35</font></i>: 
<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>
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green">E36</font></i>: 
<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>and </b><br/><a NAME="E3:1"/><i><font color="Green">E37</font></i>: 
not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">I</font>
 ;<br/>

<b>set </b><font color="Maroon">sI</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">Is</font> =  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font>;<br/>
<a NAME="E4:1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T13">SCMFSA8A:13</a></i>;<br/>
<a NAME="E5:1"/>
( <font color="Maroon">I</font> <a href="ami_1.html#K17">+*</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> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font> &amp;  <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a>, <a class="ref" href="scmfsa8c.html#T19">SCMFSA8C:19</a></i>;<br/>
<a NAME="E6:1"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">I</font> <a href="ami_1.html#K17">+*</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> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E7:1"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i>, <a class="ref" href="scmfsa7b.html#D8">SCMFSA7B:def 8</a></i>;<br/>
<a NAME="E8:1"/>
the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="xboole_0.html#R1">misses</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T13">SCMFSA_2:13</a>, <a class="ref" href="scmfsa_2.html#T14">SCMFSA_2:14</a>, <a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E9:1"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="xboole_0.html#R1">misses</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T3">SCMFSA8A:3</a></i>;<br/>
<i><font color="Green">E44</font></i>: <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="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></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="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1">SCMFSA6B:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></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="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa8a.html#T2">SCMFSA8A:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></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="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>
;<br/>
<a NAME="E11:1"/>
for <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">m</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 
<b>by </b><i>, , <a class="ref" href="scmfsa7b.html#D7">SCMFSA7B:def 7</a></i>;<br/>
<a NAME="E12:1"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font>
 
<b>by </b><i>, , <a class="ref" href="sf_mastr.html#T69">SF_MASTR:69</a></i>;<br/>
<a NAME="E13:1"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></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="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</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="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8b.html#T5">SCMFSA8B:5</a></i>;<br/>
<a NAME="E14:1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <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">b</font>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>;<br/>
<b>hence </b><a NAME="E15:1"/>
<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="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <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">b</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>;<br/>


</div>
