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

<b>set </b><font color="Maroon">A</font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>
<b>set </b><font color="Maroon">D</font> = <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> ;<br/>
<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>, <font color="Maroon">J</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">I0</font> =  <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font>;<br/>
<b>set </b><font color="Maroon">I1</font> = <font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ;<br/>
<b>set </b><font color="Maroon">s00</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <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>set </b><font color="Maroon">s3</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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>set </b><font color="Maroon">s4</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1;<br/>
<b>set </b><font color="Maroon">C3</font> =  <a href="ami_1.html#K10">Computation</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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">i</font> = <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:63"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>assume </b><a NAME="E2:63"/><i><font color="Green">E32</font></i>: 
 <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font> <a href="scmfsa8a.html#R1">is_pseudo-closed_on</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E3:63"/><i><font color="Green">E33</font></i>: 
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> 
 
<b>by </b><i><a class="ref" href="scmfsa8b.html#D1">SCMFSA8B:def 1</a></i>;<br/>
<a NAME="E4:63"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <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"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <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="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E5:63"/>
<font color="Maroon">s</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="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"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</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="scmfsa8a.html#T11">SCMFSA8A:11</a></i>;<br/>
<a NAME="E6:63"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font> <a href="scmfsa8a.html#R1">is_pseudo-closed_on</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <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="scmfsa8c.html#T11" target="_self">Th11</a>, </i>;<br/>
<a NAME="E7:63"/><i><font color="Green">E45</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E9:63"><i><font color="Green">E46</font></i></a></i>;<br/>
<a NAME="E8:63"/>
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <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>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E9:63"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E10:63"/><i><font color="Green">E48</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="sf_mastr.html#T65">SF_MASTR:65</a></i>;<br/>
<div><i><font color="Green">E49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="ref" href="sf_mastr.html#T66">SF_MASTR:66</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>now </b></a><div class="add"><b>thus </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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa8c.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa6b.html#T7">SCMFSA6B:7</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T9" target="_self">Th9</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E13:63"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="ami_1.html#K8">CurInstr</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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>;<br/>
<div><i><font color="Green">E51</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_3"><b>now </b></a><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E52</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4"><b>now </b></a><div class="add"><b>thus </b> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D5">SCMFSA6A:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmfsa8a.html#T29">SCMFSA8A:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6">SCMFSA7B:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/></div><b>end;</b></div>
<a NAME="E16:63"/>
( not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> )
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T12">SCMFSA6B:12</a>, <a class="ref" href="scmfsa_2.html#T66">SCMFSA_2:66</a></i>;<br/>
<a NAME="E17:63"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E18:63"/><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <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"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E19:63"/>
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <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>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E20:63"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E21:63"/>
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmfsa6a.html#T62">SCMFSA6A:62</a></i>;<br/>
<a NAME="E22:63"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font>
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T16" target="_self">Th16</a>, <a class="txt" href="scmfsa8c.html#E7:63"><i><font color="Green">E45</font></i></a></i>;<br/>
<a NAME="E23:63"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</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"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="scmfsa8c.html#T18" target="_self">Th18</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E24:63"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1
 
<b>by </b><i><a class="ref" href="ami_5.html#T64">AMI_5:64</a></i>;<br/>
<a NAME="E25:63"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1
 
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>;<br/>
<a NAME="E26:63"/>
 <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> 
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T55">SCMFSA6A:55</a></i>;<br/>
<a NAME="E27:63"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E28:63"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<div><i><font color="Green">E101</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_5"><b>now </b></a><div class="add"><b>thus </b> <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T15" target="_self">Th15</a>, <a class="ref" href="scmfsa8c.html#T17" target="_self">Th17</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E30:63"/>
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <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>,<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T14">SCMFSA8A:14</a></i>;<br/>
<a NAME="E31:63"/><b>then </b><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</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> <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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</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="scmfsa6a.html#T39">SCMFSA6A:39</a></i>;<br/>
<div><i><font color="Green">E104</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>thus </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"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T15" target="_self">Th15</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </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"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T15" target="_self">Th15</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E34:63"/><b>then </b><i><font color="Green">E105</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</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> <a href="hidden.html#R1">=</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</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="scmfsa8c.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>;<br/>
<a NAME="E35:63"/>
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <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"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E36:63"/><b>then </b><i><font color="Green">E106</font></i>: 
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="scmfsa6b.html#T5">SCMFSA6B:5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_8"><b>now </b></a><div class="add"><b>thus </b> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T14">SCMFSA8B:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/></div><b>end;</b></div>
<a NAME="E38:63"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E39:63"/><b>then </b><i><font color="Green">E107</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</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="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/>
<div><i><font color="Green">E108</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_9"><b>now </b></a><div class="add"><b>thus </b> <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></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="scmfsa8a.html#K3">pseudo-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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
 <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"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <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></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T12" target="_self">Th12</a>, , <a class="ref" href="scmfsa8c.html#T20" target="_self">Th20</a>, <a class="ref" href="scmfsa8c.html#T22" target="_self">Th22</a>, <a class="ref" href="scmfsa8c.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa8c.html#T8" target="_self">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">s</font>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, <a class="ref" href="scmfsa8a.html#D5">SCMFSA8A:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8a.html#T34">SCMFSA8A:34</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>

;<br/></div><b>end;</b></div>
<b>then </b><i><font color="Green">E109</font></i>:  <a href="ami_1.html#K8">CurInstr</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></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="scmfsa8a.html#K3">pseudo-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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></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="scmfsa8a.html#K3">pseudo-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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa8c.html#T27" target="_self">Th27</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E15:63"><i><font color="Green">E52</font></i></a></i>
;<br/>
<a NAME="E42:63"/><b>then </b><i><font color="Green">E119</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/>
<b>hence </b><a NAME="E43:63"/>
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="scmfsa7b.html#R6">is_halting_on</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#D8">SCMFSA7B:def 8</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_11"><b>now </b></a><div class="add"><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> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_11_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_11_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0 or ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 ) or ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_11_1_1"><b>suppose </b></a><a NAME="E1:63_11_1_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:63_11_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</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="ami_1.html#D19">AMI_1:def 19</a></i>;<br/><a NAME="E3:63_11_1_1"/><b>then </b>
 <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:63_11_1_1"/>
 <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">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="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E9:63"><i><font color="Green">E46</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_11_1_2"><b>suppose </b></a><a NAME="E1:63_11_1_2"/><i><font color="Green">E120</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div class="add"><a NAME="E2:63_11_1_2"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><b>then consider </b><font color="Maroon">k1</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:63_11_1_2"/><i><font color="Green">E121</font></i>: 
1 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><b>reconsider </b><font color="Maroon">k1</font> = <font color="Maroon">k1</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/><a NAME="E6:63_11_1_2"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">k1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-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"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmfsa8c.html#T33" target="_self">Th33</a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E7:63_11_1_2"/><b>then </b><i><font color="Green">E123</font></i>: 
<font color="Maroon">k1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, </i>;<br/><i><font color="Green">E124</font></i>:  <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> = 
 <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"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <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></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T33" target="_self">Th33</a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T12" target="_self">Th12</a>, , <a class="ref" href="scmfsa8c.html#T20" target="_self">Th20</a>, <a class="ref" href="scmfsa8c.html#T22" target="_self">Th22</a>, <a class="ref" href="scmfsa8c.html#T26" target="_self">Th26</a>, , <a class="ref" href="scmfsa8c.html#T8" target="_self">Th8</a></i>
;<br/><b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E10:63_11_1_2"/><i><font color="Green">E125</font></i>: 
 <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"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T21">SCMFSA_2:21</a></i>;<br/><a NAME="E11:63_11_1_2"/>
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, , , <a class="ref" href="scmfsa8a.html#T31">SCMFSA8A:31</a></i>;<br/><a NAME="E12:63_11_1_2"/><b>then </b>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><a NAME="E13:63_11_1_2"/><b>then </b>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E14:63_11_1_2"/><b>then </b><i><font color="Green">E126</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8a.html#T34">SCMFSA8A:34</a></i>;<br/> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T14">SCMFSA8B:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/><a NAME="E16:63_11_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E17:63_11_1_2"/><b>then </b>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T36" target="_self">Th36</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E18:63_11_1_2"/><b>then </b>
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></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="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><b>hence </b><a NAME="E19:63_11_1_2"/>
 <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">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="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T35" target="_self">Th35</a>, , <a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_11_1_3"><b>suppose </b></a><a NAME="E1:63_11_1_3"/>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:63_11_1_3"/>
 <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">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="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa8c.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa8c.html#T31" target="_self">Th31</a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E45:63"/>
 <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="scmfsa7b.html#R5">is_closed_on</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#D7">SCMFSA7B:def 7</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_12"><b>now </b></a><div class="add"><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> ;<br/><b>assume </b><a NAME="E1:63_12"/><i><font color="Green">E127</font></i>: 
 <a href="ami_1.html#K8">CurInstr</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/><b>assume </b><a NAME="E2:63_12"/>
not <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 ;<br/><a NAME="E3:63_12"/><b>then </b><i><font color="Green">E128</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scmfsa8a.html#K3">pseudo-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"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:63_12"/><i><font color="Green">E129</font></i>: 
 <a href="ami_1.html#K6">IC</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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 <b>by </b><i/>;<br/><a NAME="E5:63_12"/><i><font color="Green">E130</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E9:63"><i><font color="Green">E46</font></i></a></i>;<br/><a NAME="E6:63_12"/><i><font color="Green">E131</font></i>: 
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 7 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/> <a href="ami_1.html#K8">CurInstr</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> = 
 <a href="ami_1.html#K8">CurInstr</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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T9" target="_self">Th9</a></i>
;<br/><b>then consider </b><font color="Maroon">k1</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E9:63_12"/><i><font color="Green">E132</font></i>: 
<font color="Maroon">k1</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="scmfsa8c.html#T35" target="_self">Th35</a>, <a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/><b>reconsider </b><font color="Maroon">k1</font> = <font color="Maroon">k1</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/><a NAME="E11:63_12"/>
<font color="Maroon">k1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E12:63_12"/><b>then </b><i><font color="Green">E133</font></i>: 
<font color="Maroon">k1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-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"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T33" target="_self">Th33</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><i><font color="Green">E134</font></i>:  <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> = 
 <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"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <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></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T12" target="_self">Th12</a>, , <a class="ref" href="scmfsa8c.html#T20" target="_self">Th20</a>, <a class="ref" href="scmfsa8c.html#T22" target="_self">Th22</a>, <a class="ref" href="scmfsa8c.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa8c.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa8c.html#T8" target="_self">Th8</a></i>
;<br/><b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E15:63_12"/><i><font color="Green">E152</font></i>: 
 <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"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T21">SCMFSA_2:21</a></i>;<br/><a NAME="E16:63_12"/>
<font color="Maroon">k1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, <a class="ref" href="scmfsa8c.html#T36" target="_self">Th36</a>, </i>;<br/><a NAME="E17:63_12"/><b>then </b>
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, <a class="ref" href="scmfsa8c.html#T38" target="_self">Th38</a>, <a class="ref" href="scmfsa8a.html#T31">SCMFSA8A:31</a></i>;<br/><a NAME="E18:63_12"/><b>then </b>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><a NAME="E19:63_12"/><b>then </b>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E20:63_12"/><b>then </b><i><font color="Green">E153</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8a.html#T34">SCMFSA8A:34</a></i>;<br/> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T14">SCMFSA8B:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/><a NAME="E22:63_12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E23:63_12"/><b>then </b>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E25:63"><i><font color="Green">E93</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E24:63_12"/><b>then </b>
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></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="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><a NAME="E25:63_12"/><b>then </b><i><font color="Green">E154</font></i>: 
 <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">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="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T37" target="_self">Th37</a>, <a class="ref" href="scmfsa8c.html#T38" target="_self">Th38</a>, <a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>;<br/><b>set </b><font color="Maroon">J1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font>;<br/> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D5">SCMFSA6A:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8a.html#T29">SCMFSA8A:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6">SCMFSA7B:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3

;<br/><a NAME="E27:63_12"/><b>then </b>
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E25:63"><i><font color="Green">E93</font></i></a>, <a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><a NAME="E28:63_12"/><b>then </b>
 <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T37" target="_self">Th37</a>, <a class="ref" href="scmfsa8c.html#T38" target="_self">Th38</a>, <a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>;<br/><a NAME="E29:63_12"/><b>then </b><i><font color="Green">E155</font></i>: 
 <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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">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="scmfsa6a.html#K1">Directed</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T14">SCMFSA6A:14</a></i>;<br/><a NAME="E30:63_12"/>
 <a href="scmfsa6a.html#K1">Directed</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font>
 <b>by </b><i>, <a class="ref" href="scmfsa6a.html#T55">SCMFSA6A:55</a></i>;<br/><a NAME="E31:63_12"/><b>then </b><i><font color="Green">E156</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T39" target="_self">Th39</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><a NAME="E32:63_12"/><i><font color="Green">E157</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/> <a href="ami_1.html#K8">CurInstr</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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> = 
<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"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</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"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E28:63"><i><font color="Green">E94</font></i></a>, </i>
;<br/><b>hence </b><a NAME="E34:63_12"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmfsa8c.html#T41" target="_self">Th41</a>, <a class="ref" href="scmfsa8c.html#T42" target="_self">Th42</a>, <a class="ref" href="scmfsa7b.html#D6">SCMFSA7B:def 6</a></i>;<br/></div><b>end;</b></div>
<a NAME="E47:63"/><b>then </b><i><font color="Green">E158</font></i>: 
 <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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-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"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa8c.html#T32" target="_self">Th32</a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>
<a NAME="E48:63"/>
 <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</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"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, <a class="txt" href="scmfsa8c.html#E13:63"><i><font color="Green">E50</font></i></a></i>;<br/>
<b>hence </b><a NAME="E49:63"/>
 <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"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">a</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</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"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T11" target="_self">Th11</a>, , </i>;<br/>


</div>
