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

<b>let </b><font color="Maroon" title="c3">I</font> be  <a href="scmpds_5.html#V3" title="SCMPDS_5:attr.3">No-StopCode</a> <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/><b>let </b><font color="Maroon" title="c4">J</font> be  <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a> <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/><b>let </b><font color="Maroon" title="c5">s</font>, <font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>





<b>set </b><font color="Maroon" title="c8">IsI</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c3">I</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c9">spJ</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font>;<br/>
<b>set </b><font color="Maroon" title="c10">IsJ</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">IJ</font> = <font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font>;<br/>
<b>set </b><font color="Maroon" title="c12">sIJ</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c13">IsIJ</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c14">m1</font> =  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font>;<br/>
<b>set </b><font color="Maroon" title="c15">sm</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c16">s3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c17">m3</font> =  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c18">sE</font> =  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s</font>;<br/>
<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E36">A1</font></i>: 
( <font color="Maroon" title="c3">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c5">s</font> &amp; <font color="Maroon" title="c3">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c5">s</font> &amp; <font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s</font> &amp; <font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s</font> &amp; <font color="Maroon" title="c7">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c7">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">J</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</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="scmpds_4.html#T46" title="SCMPDS_4:th.46">SCMPDS_4:46</a></i>;<br/>
<a NAME="E3:47"/><i><font color="Green" title="E38">A3</font></i>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s2</font>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E4:47"/>
 <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T9" title="SCMPDS_4:th.9">SCMPDS_4:9</a></i>;<br/>
<a NAME="E5:47"/><b>then </b><i><font color="Green" title="E39">A4</font></i>: 
 <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s2</font>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E3:47"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E6:47"/><i><font color="Green" title="E40">A5</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T75" title="FUNCT_4:th.75">FUNCT_4:75</a></i>;<br/>
<div><i><font color="Green" title="E41">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:47_1"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span>
 ;<br/><a NAME="E2:47_1"/><b>then </b><i><font color="Green" title="E42">A7</font></i>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>;<br/><a NAME="E3:47_1"/><b>then </b><i><font color="Green" title="E43">A8</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_1_1"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span> or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  )
 </span><b>by </b><i><a class="txt" href="scmpds_7.html#E3:47_1"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="scmpds_4.html#T28" title="SCMPDS_4:th.28">SCMPDS_4:28</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1"><b>suppose </b></a><a NAME="E1:47_1_1_1"/><i><font color="Green" title="E44">A9</font></i>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:47_1_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#D40" title="AMI_1:def.40">AMI_1:def 40</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c20">l</font> = <font color="Maroon" title="c19">x</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <b>by </b><i><a class="txt" href="scmpds_7.html#E1:47_1_1_1"><i><font color="Green" title="E44">A9</font></i></a>, <a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E4:47_1_1_1"/>
<font color="Maroon" title="c20">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 ;<br/><b>hence </b><a NAME="E5:47_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</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"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E3:47_1"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="scmpds_4.html#T22" title="SCMPDS_4:th.22">SCMPDS_4:22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_2"><b>suppose </b></a><a NAME="E1:47_1_1_2"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:47_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</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"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E2:47_1"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="scmpds_3.html#T6" title="SCMPDS_3:th.6">SCMPDS_3:6</a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E8:47"/><i><font color="Green" title="E42">A10</font></i>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E9:47"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></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="E10:47"/><b>then </b><i><font color="Green" title="E43">A11</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E11:47"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/>
<a NAME="E12:47"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E10:47"><i><font color="Green" title="E43">A11</font></i></a>, <a class="ref" href="xboole_1.html#T26" title="XBOOLE_1:th.26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E13:47"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E14:47"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/>
<a NAME="E15:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E7:47"><i><font color="Green" title="E41">A6</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E16:47"/><b>then </b><i><font color="Green" title="E44">A12</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E6:47"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="lattice2.html#T8" title="LATTICE2:th.8">LATTICE2:8</a></i>;<br/>
<b>set </b><font color="Maroon" title="c19">s4</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span>;<br/>
<a NAME="E17:47"/><i><font color="Green" title="E45">A13</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="scmpds_7.html#E2:47"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="scmpds_7.html#T38" target="_self" title="SCMPDS_7:th.38">Th38</a></i>;<br/>
<a NAME="E18:47"/><i><font color="Green" title="E46">A14</font></i>: 
( <font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> &amp; <font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="scmpds_7.html#T42" target="_self" title="SCMPDS_7:th.42">Th42</a></i>;<br/>
<a NAME="E19:47"/><b>then </b><i><font color="Green" title="E47">A15</font></i>: 
<font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T38" title="SCMPDS_6:th.38">SCMPDS_6:38</a></i>;<br/>
<a NAME="E20:47"/><i><font color="Green" title="E48">A16</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E18:47"><i><font color="Green" title="E46">A14</font></i></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></i>;<br/>
<a NAME="E21:47"/>
<font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T17" target="_self" title="SCMPDS_7:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E22:47"/><i><font color="Green" title="E49">A17</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="scmpds_7.html#T44" target="_self" title="SCMPDS_7:th.44">Th44</a></i>;<br/>

<b>thus </b><a NAME="E23:47"/><i><font color="Green" title="E50">A18</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_7.html#E16:47"><i><font color="Green" title="E44">A12</font></i></a>, <a class="txt" href="scmpds_7.html#E17:47"><i><font color="Green" title="E45">A13</font></i></a>, <a class="ref" href="scmpds_4.html#T24" title="SCMPDS_4:th.24">SCMPDS_4:24</a></i>;<br/>

<b>reconsider </b><font color="Maroon" title="c20">m</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
 <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span> = 
<font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">J</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T46" title="SCMPDS_4:th.46">SCMPDS_4:46</a></i>
<br/>.= 
<font color="Maroon" title="c3">I</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span>

;<br/>
<a NAME="E26:47"/><b>then </b>
 <a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E27:47"/><b>then </b>
 <a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s2</font>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E5:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E28:47"/><i><font color="Green" title="E51">A19</font></i>: 
 <a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a></i>;<br/>

<div><i><font color="Green" title="E52">A20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:47_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c21">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c20">m</font>
 ;<br/><a NAME="E2:47_3"/><b>then </b><i><font color="Green" title="E53">A21</font></i>: 
<font color="Maroon" title="c21">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><b>assume </b><a NAME="E3:47_3"/><i><font color="Green" title="E54">A22</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c21">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 ;<br/> <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c21">k</font></span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c21">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_7.html#E8:47"><i><font color="Green" title="E42">A10</font></i></a>, <a class="txt" href="scmpds_7.html#E19:47"><i><font color="Green" title="E47">A15</font></i></a>, <a class="txt" href="scmpds_7.html#E22:47"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="scmpds_7.html#E23:47"><i><font color="Green" title="E50">A18</font></i></a>, <a class="txt" href="scmpds_7.html#E28:47"><i><font color="Green" title="E51">A19</font></i></a>, <a class="ref" href="scmpds_6.html#T45" title="SCMPDS_6:th.45">SCMPDS_6:45</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
<b>by </b><i><a class="txt" href="scmpds_7.html#E3:47_3"><i><font color="Green" title="E54">A22</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
;<br/><b>hence </b><a NAME="E5:47_3"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_7.html#E20:47"><i><font color="Green" title="E48">A16</font></i></a>, <a class="txt" href="scmpds_7.html#E2:47_3"><i><font color="Green" title="E53">A21</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/></div><b>end;</b></div>
<a NAME="E30:47"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E8:47"><i><font color="Green" title="E42">A10</font></i></a>, <a class="txt" href="scmpds_7.html#E19:47"><i><font color="Green" title="E47">A15</font></i></a>, <a class="txt" href="scmpds_7.html#E22:47"><i><font color="Green" title="E49">A17</font></i></a>, <a class="txt" href="scmpds_7.html#E23:47"><i><font color="Green" title="E50">A18</font></i></a>, <a class="txt" href="scmpds_7.html#E28:47"><i><font color="Green" title="E51">A19</font></i></a>, <a class="ref" href="scmpds_6.html#T45" title="SCMPDS_6:th.45">SCMPDS_6:45</a></i>;<br/>
<a NAME="E31:47"/><b>then </b>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p5">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p0">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></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 NAME="E32:47"/><b>then </b><i><font color="Green" title="E53">A23</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c20">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E20:47"><i><font color="Green" title="E48">A16</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:47_4"/><i><font color="Green" title="E54">A24</font></i>: 
<font color="Maroon" title="c21">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c20">m</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_4_1"/>
( <font color="Maroon" title="c21">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font> or  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c21">k</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_4_1_1"><b>suppose </b></a><a NAME="E1:47_4_1_1"/>
<font color="Maroon" title="c21">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:47_4_1_1"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c21">k</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="scmpds_7.html#T46" target="_self" title="SCMPDS_7:th.46">Th46</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_4_1_2"><b>suppose </b></a><a NAME="E1:47_4_1_2"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c21">k</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c22">kk</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:47_4_1_2"/><i><font color="Green" title="E55">A25</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c22">kk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c23">kk</font> = <font color="Maroon" title="c22">kk</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E5:47_4_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c23">kk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">k</font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E3:47_4_1_2"><i><font color="Green" title="E55">A25</font></i></a></i>;<br/><b>hence </b><a NAME="E6:47_4_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c21">k</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_7.html#E29:47"><i><font color="Green" title="E52">A20</font></i></a>, <a class="txt" href="scmpds_7.html#E1:47_4"><i><font color="Green" title="E54">A24</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E34:47"/><b>then </b><i><font color="Green" title="E54">A26</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds <br/><font color="Maroon" title="c20">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font>
 
;<br/>
<a NAME="E35:47"/>
<font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c5">s</font>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="scmpds_7.html#T43" target="_self" title="SCMPDS_7:th.43">Th43</a></i>;<br/>
<a NAME="E36:47"/><b>then </b>
<font color="Maroon" title="c7">s2</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></i>;<br/>
<a NAME="E37:47"/><b>then </b><i><font color="Green" title="E55">A27</font></i>: 
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c7">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E32:47"><i><font color="Green" title="E53">A23</font></i></a>, <a class="txt" href="scmpds_7.html#E34:47"><i><font color="Green" title="E54">A26</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/>
<a NAME="E38:47"/>
<font color="Maroon" title="c6">s1</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></i>;<br/>
<b>hence </b><a NAME="E39:47"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c7">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E37:47"><i><font color="Green" title="E55">A27</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>;<br/>


</div>
