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<b>let </b><font color="Maroon">s1</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">s2</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_4.html#V2">parahalting</a> <a href="scmpds_4.html#NM1">Program-block</a>;<br/>





<b>set </b><font color="Maroon">SI</font> =  <a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green">E37</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s1</font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green">E39</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font>
 <b>and </b><br/><a NAME="E3:18"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">s1</font>,<font color="Maroon">s2</font> <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> 
 ;<br/>

<a NAME="E4:18"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">s1</font> 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="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">l</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:18_1"/><i><font color="Green">E77</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> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">l</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><a NAME="E2:18_1"/>
 <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> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">l</font></span>)</span> <a href="hidden.html#R1">=</a>  <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> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">l</font></span>)</span>
 <b>by </b><i>, , , </i>;<br/><b>hence </b><a NAME="E3:18_1"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">l</font>
 <b>by </b><i>, , <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/></div><b>end;</b></div>
<i><font color="Green">E78</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> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s1</font></span>)</span></span>)</span> = 
 <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> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s1</font></span>)</span></span>)</span>
<b>by </b><i>, , , </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="scm_1.html#D2">SCM_1:def 2</a></i>
;<br/>
<a NAME="E7:18"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">s2</font> 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/>
<b>hence </b><a NAME="E8:18"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s2</font>
 <b>by </b><i>, , <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>

<a NAME="E9:18"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="ami_1.html#K12">Result</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>;<br/>
<a NAME="E10:18"/>
 <a href="ami_1.html#K12">Result</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>;<br/>
<b>hence </b><a NAME="E11:18"/>
 <a href="ami_1.html#K12">Result</a> <font color="Maroon">s1</font>, <a href="ami_1.html#K12">Result</a> <font color="Maroon">s2</font> <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>, , , , </i>;<br/>


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