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<b>let </b><font color="Maroon" title="c3">I</font> be   <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c5">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/>





<b>set </b><font color="Maroon" title="c6">ss</font> = <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</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/>
<b>set </b><font color="Maroon" title="c7">m</font> =  <a href="ami_1.html#K30" title="AMI_1:func.30">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</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="c3">I</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E33">A1</font></i>: 
( <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="c4">s</font> &amp; <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K30" title="AMI_1:func.30">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</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="c3">I</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:42"/><b>then </b><i><font color="Green" title="E34">A2</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</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> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></i>;<br/>
<b>assume </b><a NAME="E3:42"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</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="c3">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c5">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> 
 ;<br/>

<b>hence </b><a NAME="E4:42"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_7.html#E1:42"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="scmpds_7.html#E2:42"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/>


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