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

<b>let </b><font color="Maroon" title="c2">I</font> be  <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a> <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon" title="c3">J</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:21"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>and </b><br/><a NAME="E2:21"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c2">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>
 <b>and </b><br/><a NAME="E3:21"/><i><font color="Green" title="E10">A3</font></i>: 
<font color="Maroon" title="c3">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s</font>
 <b>and </b><br/><a NAME="E4:21"/><i><font color="Green" title="E11">A4</font></i>: 
<font color="Maroon" title="c2">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>
 <b>and </b><br/><a NAME="E5:21"/><i><font color="Green" title="E12">A5</font></i>: 
<font color="Maroon" title="c3">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c5">s1</font> = <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font>;<br/>
<b>set </b><font color="Maroon" title="c6">m1</font> =  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">C1</font> =  <a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">InJ</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font>;<br/>
<b>set </b><font color="Maroon" title="c9">s3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c10">m3</font> =  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">D</font> = <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> ;<br/>
<b>set </b><font color="Maroon" title="c12">SAt</font> =  <a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c13">JAt</font> = <font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c14">Ins</font> = the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>
<b>assume </b><a NAME="E6:21"/><i><font color="Green" title="E13">A6</font></i>: 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 ;<br/>

<a NAME="E7:21"/><i><font color="Green" title="E14">A7</font></i>: 
 <a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E8:21"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E6:21"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="scmfsa6b.html#T8" title="SCMFSA6B:th.8">SCMFSA6B:8</a></i>;<br/>
<a NAME="E9:21"/><b>then </b><i><font color="Green" title="E15">A8</font></i>: 
 <a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E7:21"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E16">A9</font></i>: <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font>
<b>by </b><i><a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T14" title="SCMFSA6B:th.14">SCMFSA6B:14</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></i>
;<br/>
<a NAME="E11:21"/><b>then </b><i><font color="Green" title="E17">A10</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E2:21"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="scmfsa7b.html#D8" title="SCMFSA7B:def.8">SCMFSA7B:def 8</a></i>;<br/>
<a NAME="E12:21"/><i><font color="Green" title="E18">A11</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E6:21"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="scmfsa6a.html#T51" title="SCMFSA6A:th.51">SCMFSA6A:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">kk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<a NAME="E14:21"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E4:21"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="sfmastr1.html#E10:21"><i><font color="Green" title="E16">A9</font></i></a>, <a class="ref" href="scmfsa8c.html#T97" title="SCMFSA8C:th.97">SCMFSA8C:97</a></i>;<br/>
<a NAME="E15:21"/><b>then </b><i><font color="Green" title="E19">A12</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E1:21"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="scmfsa8c.html#T18" title="SCMFSA8C:th.18">SCMFSA8C:18</a></i>;<br/>
<a NAME="E16:21"/><b>then </b><i><font color="Green" title="E20">A13</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c15">kk</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T75" title="FUNCT_4:th.75">FUNCT_4:75</a></i>;<br/>
<a NAME="E17:21"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="sfmastr1.html#T2" target="_self" title="SFMASTR1:th.2">Th2</a></i>;<br/>
<a NAME="E18:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E19:21"/><b>then </b><i><font color="Green" title="E21">A14</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E16:21"><i><font color="Green" title="E20">A13</font></i></a>, <a class="ref" href="lattice2.html#T8" title="LATTICE2:th.8">LATTICE2:8</a></i>;<br/>
<a NAME="E20:21"/><i><font color="Green" title="E22">A15</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">I</font>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T14" title="SCMFSA6A:th.14">SCMFSA6A:14</a></i>;<br/>
<a NAME="E21:21"/><i><font color="Green" title="E23">A16</font></i>: 
 <a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T55" title="SCMFSA6A:th.55">SCMFSA6A:55</a></i>;<br/>
<a NAME="E22:21"/>
<font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T26" title="SCMFSA6A:th.26">SCMFSA6A:26</a></i>;<br/>
<a NAME="E23:21"/><b>then </b><i><font color="Green" title="E24">A17</font></i>: 
 <a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E21:21"><i><font color="Green" title="E23">A16</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> = 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E20:21"><i><font color="Green" title="E22">A15</font></i></a>, <a class="ref" href="funct_4.html#T20" title="FUNCT_4:th.20">FUNCT_4:20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E6:21"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="lattice2.html#T8" title="LATTICE2:th.8">LATTICE2:8</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E23:21"><i><font color="Green" title="E24">A17</font></i></a>, <a class="ref" href="lattice2.html#T8" title="LATTICE2:th.8">LATTICE2:8</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font>
<b>by </b><i><a class="txt" href="sfmastr1.html#E6:21"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="lattice2.html#T8" title="LATTICE2:th.8">LATTICE2:8</a></i>
;<br/>
<a NAME="E25:21"/><b>then </b>
 <a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E26:21"/><b>then </b>
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/>
<a NAME="E27:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E9:21"><i><font color="Green" title="E15">A8</font></i></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/>
<a NAME="E28:21"/><b>then </b><i><font color="Green" title="E25">A18</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></i>;<br/>
<a NAME="E29:21"/>
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T13" title="SCMFSA_2:th.13">SCMFSA_2:13</a>, <a class="ref" href="scmfsa_2.html#T14" title="SCMFSA_2:th.14">SCMFSA_2:14</a>, <a class="ref" href="xboole_1.html#T70" title="XBOOLE_1:th.70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E30:21"/><b>then </b><i><font color="Green" title="E26">A19</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T3" title="SCMFSA8A:th.3">SCMFSA8A:3</a></i>;<br/>
<i><font color="Green" title="E27">A20</font></i>: <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1" title="SCMFSA6B:def.1">SCMFSA6B:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E30:21"><i><font color="Green" title="E26">A19</font></i></a>, <a class="ref" href="funct_4.html#T94" title="FUNCT_4:th.94">FUNCT_4:94</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E11:21"><i><font color="Green" title="E17">A10</font></i></a>, <a class="txt" href="sfmastr1.html#E12:21"><i><font color="Green" title="E18">A11</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>
;<br/>
<a NAME="E32:21"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E15:21"><i><font color="Green" title="E19">A12</font></i></a>, <a class="ref" href="scmfsa8a.html#T11" title="SCMFSA8A:th.11">SCMFSA8A:11</a></i>;<br/>
<a NAME="E33:21"/><b>then </b><i><font color="Green" title="E28">A21</font></i>: 
<font color="Maroon" title="c3">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E5:21"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="scmfsa8b.html#T6" title="SCMFSA8B:th.6">SCMFSA8B:6</a></i>;<br/>
<a NAME="E34:21"/>
<font color="Maroon" title="c3">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E3:21"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="sfmastr1.html#E5:21"><i><font color="Green" title="E12">A5</font></i></a>, <a class="txt" href="sfmastr1.html#E31:21"><i><font color="Green" title="E27">A20</font></i></a>, <a class="ref" href="scmfsa8b.html#T8" title="SCMFSA8B:th.8">SCMFSA8B:8</a></i>;<br/>
<a NAME="E35:21"/><b>then </b><i><font color="Green" title="E29">A22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E15:21"><i><font color="Green" title="E19">A12</font></i></a>, <a class="ref" href="scmfsa7b.html#D8" title="SCMFSA7B:def.8">SCMFSA7B:def 8</a></i>;<br/>
<b>set </b><font color="Maroon" title="c16">s4</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<a NAME="E36:21"/><i><font color="Green" title="E30">A23</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E6:21"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="scmfsa6b.html#T8" title="SCMFSA6B:th.8">SCMFSA6B:8</a></i>;<br/>
<a NAME="E37:21"/>
 <a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T55" title="SCMFSA6A:th.55">SCMFSA6A:55</a></i>;<br/>
<a NAME="E38:21"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_circ.html#T3" title="PRE_CIRC:th.3">PRE_CIRC:3</a></i>;<br/>
<a NAME="E39:21"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E36:21"><i><font color="Green" title="E30">A23</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E40:21"/><b>then </b><i><font color="Green" title="E31">A24</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/>
<b>hence </b><a NAME="E41:21"/><i><font color="Green" title="E32">A25</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span>
 <b>by </b><i><a class="txt" href="sfmastr1.html#E2:21"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="sfmastr1.html#E4:21"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="sfmastr1.html#E10:21"><i><font color="Green" title="E16">A9</font></i></a>, <a class="ref" href="scmfsa8a.html#T36" title="SCMFSA8A:th.36">SCMFSA8A:36</a></i>;<br/>

<b>thus </b><a NAME="E42:21"/><i><font color="Green" title="E33">A26</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="sfmastr1.html#E2:21"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="sfmastr1.html#E4:21"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="sfmastr1.html#E10:21"><i><font color="Green" title="E16">A9</font></i></a>, <a class="txt" href="sfmastr1.html#E19:21"><i><font color="Green" title="E21">A14</font></i></a>, <a class="txt" href="sfmastr1.html#E40:21"><i><font color="Green" title="E31">A24</font></i></a>, <a class="ref" href="scmfsa8a.html#T36" title="SCMFSA8A:th.36">SCMFSA8A:36</a></i>;<br/>

<b>reconsider </b><font color="Maroon" title="c17">m</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E44:21"/>
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E45:21"/><b>then </b><i><font color="Green" title="E34">A27</font></i>: 
<font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T8" title="SCMFSA6B:th.8">SCMFSA6B:8</a></i>;<br/>
<a NAME="E46:21"/>
<font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T26" title="SCMFSA6A:th.26">SCMFSA6A:26</a></i>;<br/>
<a NAME="E47:21"/><b>then </b><i><font color="Green" title="E35">A28</font></i>: 
<font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E6:21"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E48:21"/>
<font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c3">J</font>,<span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#D4" title="SCMFSA6A:def.4">SCMFSA6A:def 4</a></i>;<br/>
<a NAME="E49:21"/><b>then </b>
 <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c3">J</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c3">J</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E50:21"/><b>then </b>
 <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c3">J</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E47:21"><i><font color="Green" title="E35">A28</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E51:21"/><i><font color="Green" title="E36">A29</font></i>: 
 <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c3">J</font>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a></i>;<br/>

<a NAME="E52:21"/><i><font color="Green" title="E37">A30</font></i>: 
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T45" title="SCMFSA6A:th.45">SCMFSA6A:45</a></i>;<br/>
<a NAME="E53:21"/>
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#D4" title="SCMFSA_2:def.4">SCMFSA_2:def 4</a></i>;<br/>
<a NAME="E54:21"/><b>then </b><i><font color="Green" title="E38">A31</font></i>: 
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<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="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E42:21"><i><font color="Green" title="E33">A26</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E54:21"><i><font color="Green" title="E38">A31</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E52:21"><i><font color="Green" title="E37">A30</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="scmfsa6a.html#T46" title="SCMFSA6A:th.46">SCMFSA6A:46</a></i>
;<br/><br/>

<div><i><font color="Green" title="E39">A32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:21_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c18">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">m</font>
 ;<br/><a NAME="E2:21_5"/><b>then </b><i><font color="Green" title="E40">A33</font></i>: 
<font color="Maroon" title="c18">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><b>assume </b><a NAME="E3:21_5"/><i><font color="Green" title="E41">A34</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c18">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ;<br/> <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c18">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c18">k</font></span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E33:21"><i><font color="Green" title="E28">A21</font></i></a>, <a class="txt" href="sfmastr1.html#E41:21"><i><font color="Green" title="E32">A25</font></i></a>, <a class="txt" href="sfmastr1.html#E42:21"><i><font color="Green" title="E33">A26</font></i></a>, <a class="txt" href="sfmastr1.html#E45:21"><i><font color="Green" title="E34">A27</font></i></a>, <a class="txt" href="sfmastr1.html#E51:21"><i><font color="Green" title="E36">A29</font></i></a>, <a class="ref" href="scmfsa8c.html#T42" title="SCMFSA8C:th.42">SCMFSA8C:42</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="txt" href="sfmastr1.html#E3:21_5"><i><font color="Green" title="E41">A34</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
;<br/><a NAME="E5:21_5"/><b>then </b>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c18">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T124" title="SCMFSA_2:th.124">SCMFSA_2:124</a>, <a class="ref" href="scmfsa_4.html#T22" title="SCMFSA_4:th.22">SCMFSA_4:22</a></i>;<br/><a NAME="E6:21_5"/><b>then </b>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c18">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T122" title="SCMFSA_2:th.122">SCMFSA_2:122</a></i>;<br/><b>hence </b><a NAME="E7:21_5"/>
contradiction
 <b>by </b><i><a class="txt" href="sfmastr1.html#E35:21"><i><font color="Green" title="E29">A22</font></i></a>, <a class="txt" href="sfmastr1.html#E2:21_5"><i><font color="Green" title="E40">A33</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/></div><b>end;</b></div>
<a NAME="E57:21"/>
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E33:21"><i><font color="Green" title="E28">A21</font></i></a>, <a class="txt" href="sfmastr1.html#E41:21"><i><font color="Green" title="E32">A25</font></i></a>, <a class="txt" href="sfmastr1.html#E42:21"><i><font color="Green" title="E33">A26</font></i></a>, <a class="txt" href="sfmastr1.html#E45:21"><i><font color="Green" title="E34">A27</font></i></a>, <a class="txt" href="sfmastr1.html#E51:21"><i><font color="Green" title="E36">A29</font></i></a>, <a class="ref" href="scmfsa8c.html#T42" title="SCMFSA8C:th.42">SCMFSA8C:42</a></i>;<br/>
<a NAME="E58:21"/><b>then </b>
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>;<br/>
<b>then </b><i><font color="Green" title="E40">A35</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c17">m</font></span>)</span> = 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E35:21"><i><font color="Green" title="E29">A22</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T8" title="SCMFSA_4:th.8">SCMFSA_4:8</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:21_7"/><i><font color="Green" title="E41">A36</font></i>: 
<font color="Maroon" title="c18">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">m</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_7_1"/>
( <font color="Maroon" title="c18">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span> or  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c18">k</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_7_1_1"><b>suppose </b></a><a NAME="E1:21_7_1_1"/>
<font color="Maroon" title="c18">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_7_1_1"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c18">k</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="sfmastr1.html#E2:21"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="sfmastr1.html#E4:21"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="sfmastr1.html#E10:21"><i><font color="Green" title="E16">A9</font></i></a>, <a class="txt" href="sfmastr1.html#E28:21"><i><font color="Green" title="E25">A18</font></i></a>, <a class="ref" href="scmfsa8a.html#T35" title="SCMFSA8A:th.35">SCMFSA8A:35</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_7_1_2"><b>suppose </b></a><a NAME="E1:21_7_1_2"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c18">k</font>
 ;<br/><div class="add"><a NAME="E2:21_7_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c18">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c19">kk</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:21_7_1_2"/><i><font color="Green" title="E42">A37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">kk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c20">kk</font> = <font color="Maroon" title="c19">kk</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E6:21_7_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c20">kk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">k</font>
 <b>by </b><i><a class="txt" href="sfmastr1.html#E4:21_7_1_2"><i><font color="Green" title="E42">A37</font></i></a></i>;<br/><b>hence </b><a NAME="E7:21_7_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c18">k</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="sfmastr1.html#E56:21"><i><font color="Green" title="E39">A32</font></i></a>, <a class="txt" href="sfmastr1.html#E1:21_7"><i><font color="Green" title="E41">A36</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E61:21"/><b>then </b><i><font color="Green" title="E41">A38</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds <br/><font color="Maroon" title="c17">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font>
 
;<br/>
<b>thus </b><a NAME="E62:21"/><i><font color="Green" title="E42">A39</font></i>: 
<font color="Maroon" title="c4">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="txt" href="sfmastr1.html#E59:21"><i><font color="Green" title="E40">A35</font></i></a>, <a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a></i>;<br/>

<a NAME="E63:21"/><b>then </b><i><font color="Green" title="E43">A40</font></i>: 
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">m</font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E59:21"><i><font color="Green" title="E40">A35</font></i></a>, <a class="txt" href="sfmastr1.html#E61:21"><i><font color="Green" title="E41">A38</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/>
<b>hence </b><a NAME="E64:21"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sfmastr1.html#E11:21"><i><font color="Green" title="E17">A10</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>;<br/>

<a NAME="E65:21"/><i><font color="Green" title="E44">A41</font></i>: 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E66:21"/><b>then </b>
<font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T8" title="SCMFSA6B:th.8">SCMFSA6B:8</a></i>;<br/>
<a NAME="E67:21"/><b>then </b><i><font color="Green" title="E45">A42</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:21_8"/><i><font color="Green" title="E46">A43</font></i>: 
<font color="Maroon" title="c3">J</font> is <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>
 ;<br/><a NAME="E2:21_8"/><i><font color="Green" title="E47">A44</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="sfmastr1.html#E33:21"><i><font color="Green" title="E28">A21</font></i></a>, <a class="txt" href="sfmastr1.html#E41:21"><i><font color="Green" title="E32">A25</font></i></a>, <a class="txt" href="sfmastr1.html#E42:21"><i><font color="Green" title="E33">A26</font></i></a>, <a class="txt" href="sfmastr1.html#E45:21"><i><font color="Green" title="E34">A27</font></i></a>, <a class="txt" href="sfmastr1.html#E51:21"><i><font color="Green" title="E36">A29</font></i></a>, <a class="ref" href="scmfsa8c.html#T42" title="SCMFSA8C:th.42">SCMFSA8C:42</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c17">m</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E62:21"><i><font color="Green" title="E42">A39</font></i></a>, <a class="txt" href="sfmastr1.html#E63:21"><i><font color="Green" title="E43">A40</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E2:21_8"><i><font color="Green" title="E47">A44</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" title="SCMFSA6A:th.38">SCMFSA6A:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E33:21"><i><font color="Green" title="E28">A21</font></i></a>, <a class="txt" href="sfmastr1.html#E67:21"><i><font color="Green" title="E45">A42</font></i></a>, <a class="txt" href="sfmastr1.html#E1:21_8"><i><font color="Green" title="E46">A43</font></i></a>, <a class="ref" href="scmfsa8c.html#T97" title="SCMFSA8C:th.97">SCMFSA8C:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sfmastr1.html#E52:21"><i><font color="Green" title="E37">A30</font></i></a>, <a class="txt" href="sfmastr1.html#E65:21"><i><font color="Green" title="E44">A41</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="scmfsa6a.html#T46" title="SCMFSA6A:th.46">SCMFSA6A:46</a></i>
;<br/></div>
<b>end;</b></div>


</div>
