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<b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">J</font> being  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/> for <font color="Olive" title="b3">a</font> being <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>  <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp; <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> holds <br/>(  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> )</span><br/><b>let </b><font color="Maroon" title="c4">I</font>, <font color="Maroon" title="c5">J</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>  <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp; <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> holds <br/>(  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> )</span><br/><b>let </b><font color="Maroon" title="c6">a</font> be  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>  <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp; <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> implies (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> ) )</span><br/>





<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> or  not <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> or (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> ) )</span><br/>

<b>assume </b><a NAME="E2:20"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> or (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> ) )</span><br/>

<b>assume </b><a NAME="E3:20"/><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font> )</span><br/>

<b>set </b><font color="Maroon" title="c7">I1</font> = <font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">s1</font> = <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c9">s3</font> = <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c10">s4</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1;<br/>
<b>set </b><font color="Maroon" title="c11">i</font> = <font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>;<br/>
<a NAME="E4:20"/><i><font color="Green" title="E21">A4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E5:20"/>
<font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font>
 
<b>by </b><i><a class="txt" href="#E2:20"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="#E3:20"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="scmfsa8a.html#T46" title="SCMFSA8A:th.46">SCMFSA8A:46</a></i>;<br/>
<a NAME="E6:20"/><b>then </b><i><font color="Green" title="E22">A5</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#D8" title="SCMFSA7B:def.8">SCMFSA7B:def 8</a></i>;<br/>
<a NAME="E7:20"/><i><font color="Green" title="E23">A6</font></i>: 
<font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font>
 
<b>by </b><i><a class="txt" href="#E2:20"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="#E3:20"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="scmfsa8a.html#T46" title="SCMFSA8A:th.46">SCMFSA8A:46</a></i>;<br/>
<a NAME="E8:20"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T11" title="SCMFSA8A:th.11">SCMFSA8A:11</a></i>;<br/>
<a NAME="E9:20"/><b>then </b><i><font color="Green" title="E24">A7</font></i>: 
<font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E7:20"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="scmfsa8b.html#T6" target="_self" title="SCMFSA8B:th.6">Th6</a></i>;<br/>
<a NAME="E10:20"/><i><font color="Green" title="E25">A8</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E18"><i><font color="Green" title="E13">Lm2</font></i></a></i>;<br/>
<a NAME="E11:20"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T9" title="SCMFSA8A:th.9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E12:20"/><b>then </b><i><font color="Green" title="E26">A9</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E13:20"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sf_mastr.html#T65" title="SF_MASTR:th.65">SF_MASTR:65</a></i>;<br/>
<b>then </b><i><font color="Green" title="E27">A10</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T66" title="SF_MASTR:th.66">SF_MASTR:66</a></i>
;<br/>
<i><font color="Green" title="E28">A11</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E10:20"><i><font color="Green" title="E25">A8</font></i></a>, <a class="txt" href="#E12:20"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">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#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E10:20"><i><font color="Green" title="E25">A8</font></i></a>, <a class="ref" href="scmfsa6b.html#T7" title="SCMFSA6B:th.7">SCMFSA6B:7</a></i>
<br/>.= 
<font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E19"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E29">A12</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></i>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E14:20"><i><font color="Green" title="E27">A10</font></i></a>, <a class="txt" href="#E15:20"><i><font color="Green" title="E28">A11</font></i></a></i>
;<br/>
<i><font color="Green" title="E30">A13</font></i>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D6" title="SCMFSA6A:def.6">SCMFSA6A:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61" title="SCMFSA6A:th.61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<b>by </b><i><a class="ref" href="scmfsa8a.html#T29" title="SCMFSA8A:th.29">SCMFSA8A:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61" title="SCMFSA6A:th.61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6" title="SCMFSA7B:th.6">SCMFSA7B:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>

;<br/>
<a NAME="E18:20"/>
( not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s</font> )
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T12" title="SCMFSA6B:th.12">SCMFSA6B:12</a>, <a class="ref" href="scmfsa_2.html#T66" title="SCMFSA_2:th.66">SCMFSA_2:66</a></i>;<br/>
<a NAME="E19:20"/><b>then </b><i><font color="Green" title="E31">A14</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/>
<a NAME="E20:20"/><i><font color="Green" title="E32">A15</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E21:20"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T9" title="SCMFSA8A:th.9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E22:20"/><b>then </b><i><font color="Green" title="E33">A16</font></i>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E20:20"><i><font color="Green" title="E32">A15</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E23:20"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <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"><font color="Maroon" title="c6">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T67" title="SCMFSA6A:th.67">SCMFSA6A:67</a></i>;<br/>
<a NAME="E24:20"/><b>then </b>
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font>
 
<b>by </b><i><a class="txt" href="#E17:20"><i><font color="Green" title="E30">A13</font></i></a>, <a class="txt" href="scmfsa8b.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E25:20"/><b>then </b>
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E22:20"><i><font color="Green" title="E33">A16</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E26:20"/><b>then </b>
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1"><a href="scmnorm.html#K7" title="SCMNORM:func.7">[</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span><a href="scmnorm.html#K7" title="SCMNORM:func.7">]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1
 
<b>by </b><i><a class="ref" href="ami_1.html#T99" title="AMI_1:th.99">AMI_1:99</a></i>;<br/>
<a NAME="E27:20"/><b>then </b><i><font color="Green" title="E34">A17</font></i>: 
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1
 
<b>by </b><i><a class="ref" href="ami_1.html#T105" title="AMI_1:th.105">AMI_1:105</a></i>;<br/>
<a NAME="E28:20"/><i><font color="Green" title="E35">A18</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</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"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
 
<b>by </b><i><a class="txt" href="#E16:20"><i><font color="Green" title="E29">A12</font></i></a>, <a class="txt" href="#E19:20"><i><font color="Green" title="E31">A14</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>;<br/>
<a NAME="E29:20"/><i><font color="Green" title="E36">A19</font></i>: 
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T39" title="SCMFSA6A:th.39">SCMFSA6A:39</a>, <a class="ref" href="scmfsa8a.html#T14" title="SCMFSA8A:th.14">SCMFSA8A:14</a></i>;<br/>
<div><i><font color="Green" title="E37">A20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c12">a</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c12">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="#E29:20"><i><font color="Green" title="E36">A19</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="#E16:20"><i><font color="Green" title="E29">A12</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c12">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c12">f</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c12">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c12">f</font>
<b>by </b><i><a class="txt" href="#E29:20"><i><font color="Green" title="E36">A19</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c12">f</font>
<b>by </b><i><a class="txt" href="#E16:20"><i><font color="Green" title="E29">A12</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E32:20"/><b>then </b><i><font color="Green" title="E38">A21</font></i>: 
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 
<b>by </b><i><a class="txt" href="#E30:20"><i><font color="Green" title="E37">A20</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" title="SCMFSA6A:th.38">SCMFSA6A:38</a></i>;<br/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p0">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></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/>.= 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p0">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="#E4:20"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="#E9:20"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="#E27:20"><i><font color="Green" title="E34">A17</font></i></a>, <a class="txt" href="#E28:20"><i><font color="Green" title="E35">A18</font></i></a>, <a class="txt" href="#E32:20"><i><font color="Green" title="E38">A21</font></i></a>, <a class="ref" href="scmfsa8b.html#T11" target="_self" title="SCMFSA8B:th.11">Th11</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">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"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="#E6:20"><i><font color="Green" title="E22">A5</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/>
<a NAME="E34:20"/><b>then </b><i><font color="Green" title="E39">A22</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_8_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_8_1"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">k</font> or <font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_8_1_1"><b>suppose </b></a><a NAME="E1:20_8_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c13">k1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:20_8_1_1"/><i><font color="Green" title="E40">A23</font></i>: 
<font color="Maroon" title="c13">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c14">k1</font> = <font color="Maroon" title="c13">k1</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/><b>reconsider </b><font color="Maroon" title="c15">m</font> =  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c14">k1</font></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>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E6:20_8_1_1"/><i><font color="Green" title="E41">A25</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T61" title="SCMFSA6A:th.61">SCMFSA6A:61</a>, <a class="ref" href="scmfsa8a.html#T17" title="SCMFSA8A:th.17">SCMFSA8A:17</a></i>;<br/><i><font color="Green" title="E42">A26</font></i>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
<b>by </b><i><a class="ref" href="scmfsa8b.html#T14" target="_self" title="SCMFSA8B:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:20_8_1_1"><i><font color="Green" title="E41">A25</font></i></a></i>
;<br/><a NAME="E8:20_8_1_1"/>
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c15">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:20"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="scmfsa7b.html#D7" title="SCMFSA7B:def.7">SCMFSA7B:def 7</a></i>;<br/><a NAME="E9:20_8_1_1"/><b>then </b>
<font color="Maroon" title="c15">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15" title="SCMFSA6A:th.15">SCMFSA6A:15</a></i>;<br/><a NAME="E10:20_8_1_1"/><b>then </b><i><font color="Green" title="E43">A27</font></i>: 
<font color="Maroon" title="c15">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:20_8_1_1"><i><font color="Green" title="E42">A26</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">k</font></span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<font color="Maroon" title="c14">k1</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:20_8_1_1"><i><font color="Green" title="E40">A23</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:20"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="#E9:20"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="#E27:20"><i><font color="Green" title="E34">A17</font></i></a>, <a class="txt" href="#E28:20"><i><font color="Green" title="E35">A18</font></i></a>, <a class="txt" href="#E32:20"><i><font color="Green" title="E38">A21</font></i></a>, <a class="ref" href="scmfsa8b.html#T11" target="_self" title="SCMFSA8B:th.11">Th11</a></i>
;<br/><b>hence </b><a NAME="E12:20_8_1_1"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E10:20_8_1_1"><i><font color="Green" title="E43">A27</font></i></a>, <a class="ref" href="scmfsa6a.html#T15" title="SCMFSA6A:th.15">SCMFSA6A:15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_8_1_2"><b>suppose </b></a><a NAME="E1:20_8_1_2"/>
<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span></span><br/><div class="add"><b>hence </b><a NAME="E2:20_8_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E10:20"><i><font color="Green" title="E25">A8</font></i></a>, <a class="txt" href="#E14:20"><i><font color="Green" title="E27">A10</font></i></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E36:20"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c3">s</font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#D7" title="SCMFSA7B:def.7">SCMFSA7B:def 7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font></span><br/>

<b>thus </b><a NAME="E37:20"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c3">s</font>
 <b>by </b><i><a class="txt" href="#E34:20"><i><font color="Green" title="E39">A22</font></i></a>, <a class="ref" href="scmfsa7b.html#D8" title="SCMFSA7B:def.8">SCMFSA7B:def 8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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