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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>



<b>set </b><font color="Maroon">pi</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">A</font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>
<a NAME="E1:9"/><i><font color="Green">E37</font></i>: 
 <a href="card_1.html#K4">card</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="hidden.html#R1">=</a> 2
 
<b>by </b><i/>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:9_1"/><i><font color="Green">E39</font></i>: 
<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"><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>
 ;<br/><a NAME="E2:9_1"/>
 <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> <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="ami_3.html#D13">AMI_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:9_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="scmpds_3.html#T32">SCMPDS_3:32</a></i>;<br/><a NAME="E5:9_1"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, , , <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/><a NAME="E6:9_1"/><b>then </b>
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E7:9_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 1 )
 <b>by </b><i>, <a class="ref" href="cqc_the1.html#T2">CQC_THE1:2</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:9"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 1 )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:9_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 1 )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2_1"><b>suppose </b></a><a NAME="E1:9_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:9_2_1"/>
<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"><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_4.html#T1">SCMPDS_4:1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2_2"><b>suppose </b></a><a NAME="E1:9_2_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:9_2_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"><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_4.html#T1">SCMPDS_4:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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