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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="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/>





<b>set </b><font color="Maroon">s0</font> =  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">sw</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> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span></span>)</span>;<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">s0I</font> = <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>;<br/>
<b>set </b><font color="Maroon">s0w</font> = <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"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span> <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>;<br/>
<b>assume </b><a NAME="E1:20"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">I</font> <a href="scm_halt.html#R1">is_closed_onInit</a> <font color="Maroon">s</font>
 ;<br/>

<b>assume </b><a NAME="E2:20"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">I</font> <a href="scm_halt.html#R2">is_halting_onInit</a> <font color="Maroon">s</font>
 ;<br/>

<b>assume </b><a NAME="E3:20"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">s</font> <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="E4:20"/><i><font color="Green">E45</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>by </b><i>, <a class="ref" href="scm_halt.html#T40">SCM_HALT:40</a></i>;<br/>
<a NAME="E5:20"/><i><font color="Green">E47</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>by </b><i>, <a class="ref" href="scm_halt.html#T41">SCM_HALT:41</a></i>;<br/>
<a NAME="E6:20"/><i><font color="Green">E49</font></i>: 
<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> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>;<br/>
<a NAME="E7:20"/><i><font color="Green">E50</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="E8:20"/><i><font color="Green">E51</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> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span></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"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span> <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/>
<b>hence </b><a NAME="E9:20"/>
 <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> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 <b>by </b><i>, , , , <a class="ref" href="scmfsa_9.html#T47">SCMFSA_9:47</a></i>;<br/>

<b>thus </b><a NAME="E10:20"/>
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</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="nat_1.html#K1">+</a> 3 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> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">k</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span>
 <b>by </b><i>, , , , , <a class="ref" href="scmfsa_9.html#T47">SCMFSA_9:47</a></i>;<br/>


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