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<b>let </b><font color="Maroon" title="c6">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<b>given </b><font color="Maroon" title="c7">s</font> being   <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> <b> such that </b><a NAME="E2:87"/><i><font color="Green" title="E41">A1</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c7">s</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E3:87"/><i><font color="Green" title="E42">A2</font></i>: 
<font color="Maroon" title="c6">I</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 ;<br/>

<a NAME="E4:87"/><i><font color="Green" title="E43">A3</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T6" target="_self" title="SCMPDS_2:th.6">Tx</a></i>;<br/>
<a NAME="E5:87"/><i><font color="Green" title="E44">A4</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E3:87"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a>, <a class="ref" href="scmpds_2.html#T6" target="_self" title="SCMPDS_2:th.6">Tx</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">w</font> = <font color="Maroon" title="c7">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  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_2.html#E4:87"><i><font color="Green" title="E43">A3</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">mj</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E8:87"/><i><font color="Green" title="E45">A5</font></i>: 
( <font color="Maroon" title="c9">mj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w</font> &amp;  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c9">mj</font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D19" target="_self" title="SCMPDS_2:def.19">Def19</a></i>;<br/>
<b>thus </b><a NAME="E9:87"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E2:87"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="scmpds_2.html#E5:87"><i><font color="Green" title="E44">A4</font></i></a>, <a class="txt" href="scmpds_2.html#E8:87"><i><font color="Green" title="E45">A5</font></i></a>, <a class="txt" href="scmpds_2.html#E4:87"><i><font color="Green" title="E43">A3</font></i></a></i>;<br/>


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