<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c1">D</font> = <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> ;<br/>
<b>let </b><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c3">I</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/>



<b>set </b><font color="Maroon" title="c4">I0</font> =  <a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c3">I</font>;<br/>
<b>set </b><font color="Maroon" title="c5">I1</font> = <font color="Maroon" title="c3">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">SCM+FSA-Stop</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">s2</font> = <font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">s10</font> = <font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">k</font> =  <a href="scmfsa8a.html#K3" title="SCMFSA8A:func.3">pseudo-LifeSpan</a> <font color="Maroon" title="c2">s</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c3">I</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:56"/>
 <a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c3">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c2">s</font>
 ;<br/>

<a NAME="E2:56"/><b>then </b><i><font color="Green" title="E52">A1</font></i>: 
( <font color="Maroon" title="c3">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">SCM+FSA-Stop</a>  <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c2">s</font> &amp;  <a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa8a.html#K3" title="SCMFSA8A:func.3">pseudo-LifeSpan</a> <font color="Maroon" title="c2">s</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c3">I</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K3" title="SCMFSA8A:func.3">pseudo-LifeSpan</a> <font color="Maroon" title="c2">s</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K3" title="SCMFSA8A:func.3">pseudo-LifeSpan</a> <font color="Maroon" title="c2">s</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T58" target="_self" title="SCMFSA8C:th.58">Th58</a></i>;<br/>
<a NAME="E3:56"/><b>then </b>
<font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#D8" title="SCMFSA7B:def.8">SCMFSA7B:def 8</a></i>;<br/>
<b>hence </b><a NAME="E4:56"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K3" title="SCMFSA8A:func.3">pseudo-LifeSpan</a> <font color="Maroon" title="c2">s</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E2:56"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="scmfsa6b.html#T16" title="SCMFSA6B:th.16">SCMFSA6B:16</a></i>;<br/>


</div>
