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

<b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">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="c5">a</font> be  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>  <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>let </b><font color="Maroon" title="c6">I</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<b>set </b><font color="Maroon" title="c7">Is</font> =  <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c4">s</font>;<br/>
<b>set </b><font color="Maroon" title="c8">WH</font> =  <a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font>;<br/>
<b>set </b><font color="Maroon" title="c9">Ins</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>
<b>set </b><font color="Maroon" title="c10">Ids</font> = <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span></span>)</span>;<br/>
<a NAME="E3:26"/>
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c4">s</font></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"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">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="scmfsa8b.html#T5" title="SCMFSA8B:th.5">SCMFSA8B:5</a></i>;<br/>
<b>then </b><i><font color="Green" title="E26">A3</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">a</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T38" title="SCMFSA6A:th.38">SCMFSA6A:38</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>
;<br/>
<a NAME="E5:26"/><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T13" title="SCMFSA8A:th.13">SCMFSA8A:13</a></i>;<br/>
<a NAME="E6:26"/><b>then </b><i><font color="Green" title="E28">A5</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:26"/>
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>;<br/>
<a NAME="E8:26"/><b>then </b>
 <a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="scmfsa9a.html#E2:26"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="scmfsa_9.html#T18" title="SCMFSA_9:th.18">SCMFSA_9:18</a></i>;<br/>
<a NAME="E9:26"/><b>then </b><i><font color="Green" title="E29">A6</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmfsa9a.html#E5:26"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="scmfsa7b.html#D8" title="SCMFSA7B:def.8">SCMFSA7B:def 8</a></i>;<br/>
<a NAME="E10:26"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <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> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T13" title="SCMFSA_2:th.13">SCMFSA_2:13</a>, <a class="ref" href="scmfsa_2.html#T14" title="SCMFSA_2:th.14">SCMFSA_2:14</a>, <a class="ref" href="xboole_1.html#T70" title="XBOOLE_1:th.70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E11:26"/><b>then </b><i><font color="Green" title="E30">A7</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <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> 
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T3" title="SCMFSA8A:th.3">SCMFSA8A:3</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c4">s</font></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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </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="scmfsa6b.html#D1" title="SCMFSA6B:def.1">SCMFSA6B:def 1</a></i>
<br/>.= 
<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="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></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>
<b>by </b><i><a class="txt" href="scmfsa9a.html#E11:26"><i><font color="Green" title="E30">A7</font></i></a>, <a class="ref" href="funct_4.html#T94" title="FUNCT_4:th.94">FUNCT_4:94</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">I</font></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>
<b>by </b><i><a class="txt" href="scmfsa9a.html#E9:26"><i><font color="Green" title="E29">A6</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">while=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">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="scmfsa9a.html#E2:26"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="scmfsa9a.html#E4:26"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmfsa9a.html#E6:26"><i><font color="Green" title="E28">A5</font></i></a>, <a class="ref" href="scmfsa9a.html#T22" target="_self" title="SCMFSA9A:th.22">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c4">s</font></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="scmfsa8b.html#T5" title="SCMFSA8B:th.5">SCMFSA8B:5</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <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="scmfsa9a.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="scmfsa8c.html#T27" title="SCMFSA8C:th.27">SCMFSA8C:27</a></i>
;<br/>


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