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

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">i</font> be  <a href="scmpds_5.html#V2" target="_self">parahalting</a> <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>



<b>set </b><font color="Maroon">Li</font> =  <a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">Mi</font> =  <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">sI</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">Is</font> =  <a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">SA0</font> =  <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>;<br/>
<b>set </b><font color="Maroon">IC1</font> =  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span>;<br/>
<a NAME="E1:69"/><i><font color="Green">E37</font></i>: 
(  <a href="scmpds_3.html#K2">inspos</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:69"/><i><font color="Green">E39</font></i>: 
(  <a href="scmpds_3.html#K2">inspos</a> 1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:69"/><i><font color="Green">E40</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E4:69"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T63">SCMPDS_4:63</a></i>;<br/>
<div><i><font color="Green">E76</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:69_1"/><i><font color="Green">E77</font></i>: 
 <a href="ami_1.html#K12">Result</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><b>set </b><font color="Maroon">X</font> = <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>;<br/><b>set </b><font color="Maroon">Y</font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><a NAME="E2:69_1"/><i><font color="Green">E78</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E3:69_1"/><i><font color="Green">E79</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E4:69_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T15">FUNCT_4:15</a></i>;<br/><a NAME="E5:69_1"/>
<font color="Maroon">s</font>,<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T27">SCMFSA6A:27</a></i>;<br/><a NAME="E6:69_1"/><b>then </b>
 <a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font>,<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i>, <a class="ref" href="scmfsa6a.html#T11">SCMFSA6A:11</a></i>;<br/><a NAME="E7:69_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E8:69_1"/><b>then </b><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T7">SCMPDS_3:7</a></i>;<br/><a NAME="E9:69_1"/><i><font color="Green">E89</font></i>: 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#R1">misses</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:69_1_1"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#NR5" target="_self">meets</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:69_1_1"/><i><font color="Green">E90</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:69_1_1"/><i><font color="Green">E91</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1"><b>suppose </b></a><a NAME="E1:69_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_1_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmpds_2.html#T10">SCMPDS_2:10</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_2"><b>suppose </b></a><a NAME="E1:69_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_1_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="ami_1.html#T48">AMI_1:48</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E10:69_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T87">RELAT_1:87</a></i>;<br/><a NAME="E11:69_1"/><b>then </b><i><font color="Green">E92</font></i>: 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T13" target="_self">Th13</a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/><a NAME="E12:69_1"/><i><font color="Green">E93</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E13:69_1"/><i><font color="Green">E94</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>;<br/><a NAME="E14:69_1"/><i><font color="Green">E129</font></i>: 
the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 ;<br/><a NAME="E15:69_1"/><i><font color="Green">E142</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, , <a class="ref" href="funct_4.html#T76">FUNCT_4:76</a></i>;<br/><a NAME="E16:69_1"/><i><font color="Green">E143</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, , <a class="ref" href="scmpds_5.html#T14" target="_self">Th14</a>, <a class="ref" href="scmpds_5.html#T15" target="_self">Th15</a>, <a class="ref" href="scmfsa6b.html#T3">SCMFSA6B:3</a>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_2"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:69_1_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="subset_1.html#K9">/\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i>, <a class="ref" href="scmpds_5.html#T14" target="_self">Th14</a>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:69_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 ;<br/><a NAME="E3:69_1_2"/><b>then </b><i><font color="Green">E144</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>;<br/><a NAME="E4:69_1_2"/><b>then </b><i><font color="Green">E145</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T21">XBOOLE_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <b>by </b><i>, <a class="ref" href="xboole_1.html#T21">XBOOLE_1:21</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T16" target="_self">Th16</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">x'</font>
<b>by </b><i><a class="ref" href="ami_1.html#D13">AMI_1:def 13</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T3" target="_self">Th3</a></i>
;<br/></div><b>end;</b></div><a NAME="E18:69_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/><a NAME="E19:69_1"/><b>then </b><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 <b>by </b><i>, , , <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><b>thus </b> <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T98">RELAT_1:98</a>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>
<br/>.= 
 <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T11" target="_self">Th11</a>, , <a class="ref" href="relat_1.html#T98">RELAT_1:98</a>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>
;<br/></div><b>end;</b></div>
<i><font color="Green">E147</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/>
<a NAME="E7:69"/><i><font color="Green">E148</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_4.html#D9">SCMPDS_4:def 9</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_3"/>
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0 or  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 1 )
 </span><b>by </b><i>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1"><b>suppose </b></a><a NAME="E1:69_3_1"/><i><font color="Green">E149</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0
 ;<br/><div class="add"><b>then </b><i><font color="Green">E150</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, <a class="ref" href="ami_1.html#D13">AMI_1:def 13</a></i>
<br/>.= 
<font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/><a NAME="E3:69_3_1"/><i><font color="Green">E151</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0
 <b>by </b><i><a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, <a class="ref" href="scmpds_5.html#T11" target="_self">Th11</a></i>;<br/><i><font color="Green">E152</font></i>:  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> 1

;<br/><b>set </b><font color="Maroon">Ni</font> =  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font>;<br/><a NAME="E5:69_3_1"/>
 <a href="scmpds_3.html#K2">inspos</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_3.html#K2">inspos</a> 1
 <b>by </b><i><a class="ref" href="scmpds_3.html#T31">SCMPDS_3:31</a></i>;<br/><a NAME="E6:69_3_1"/><b>then </b><i><font color="Green">E153</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,1,4,5,6</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i>, <a class="ref" href="scmpds_5.html#T13" target="_self">Th13</a>, <a class="ref" href="scmpds_4.html#T6">SCMPDS_4:6</a></i>;<br/><a NAME="E7:69_3_1"/><i><font color="Green">E154</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>by </b><i/>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_3_1_3_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a>  or <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1_1"><b>suppose </b></a><a NAME="E1:69_3_1_3_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_3_1_3_1_1"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T8" target="_self">Th8</a>, <a class="ref" href="scmpds_5.html#T9" target="_self">Th9</a>, <a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, , <a class="ref" href="ami_1.html#D22">AMI_1:def 22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1_2"><b>suppose </b></a><a NAME="E1:69_3_1_3_1_2"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><div class="add"><a NAME="E2:69_3_1_3_1_2"/><i><font color="Green">E156</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, <a class="ref" href="scmpds_5.html#T11" target="_self">Th11</a>, </i>;<br/><div><i><font color="Green">E157</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3_1_3_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_3_1_3_1_2_1_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 )
 </span><b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:69_3_1_3_1_2_1_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:69_3_1_3_1_2_1_1_1"/><i><font color="Green">E158</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K4">goto</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T35">SCMPDS_2:35</a></i>;<br/><b>thus </b><a NAME="E4:69_3_1_3_1_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:69_3_1_3_1_2_1_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:69_3_1_3_1_2_1_1_2"/><i><font color="Green">E159</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K8">&lt;&gt;0_goto</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T39">SCMPDS_2:39</a></i>;<br/><b>thus </b><a NAME="E4:69_3_1_3_1_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:69_3_1_3_1_2_1_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:69_3_1_3_1_2_1_1_3"/><i><font color="Green">E160</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T40">SCMPDS_2:40</a></i>;<br/><b>thus </b><a NAME="E4:69_3_1_3_1_2_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_3_1_2_1_1_4"><b>suppose </b></a><a NAME="E1:69_3_1_3_1_2_1_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:69_3_1_3_1_2_1_1_4"/><i><font color="Green">E161</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T41">SCMPDS_2:41</a></i>;<br/><b>thus </b><a NAME="E4:69_3_1_3_1_2_1_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E4:69_3_1_3_1_2"/>
for <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  holds  <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Olive">loc</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Olive">loc</font>
 <b>by </b><i><a class="ref" href="ami_1.html#D13">AMI_1:def 13</a></i>;<br/><a NAME="E5:69_3_1_3_1_2"/><b>then </b><i><font color="Green">E162</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T15" target="_self">Th15</a>, , <a class="ref" href="scmpds_2.html#T54">SCMPDS_2:54</a></i>;<br/><i><font color="Green">E163</font></i>:  <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3_1_3_1_2_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">n</font> = 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/><b>hence </b><a NAME="E2:69_3_1_3_1_2_3"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i>, <a class="ref" href="scmpds_5.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div><a NAME="E8:69_3_1_3_1_2"/><b>then </b>
not <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/><b>hence </b><a NAME="E9:69_3_1_3_1_2"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_4.html#T63">SCMPDS_4:63</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_2"><b>suppose </b></a><a NAME="E1:69_3_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 1
 ;<br/><div class="add"><b>then </b> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, <a class="ref" href="ami_1.html#D13">AMI_1:def 13</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/><b>hence </b><a NAME="E3:69_3_2"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1" target="_self">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T8" target="_self">Th8</a>, <a class="ref" href="scmpds_5.html#T9" target="_self">Th9</a>, <a class="ref" href="scmpds_5.html#T10" target="_self">Th10</a>, <a class="ref" href="ami_1.html#D22">AMI_1:def 22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
