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<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</font> be   <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> ;<br/><b>let </b><font color="Maroon" title="c3">I</font> be  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a> <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/>





<b>set </b><font color="Maroon" title="c4">SI</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c3">I</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green" title="E21">A1</font></i>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">s1</font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s2</font>
 <b>and </b><br/><a NAME="E3:18"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 ;<br/>

<a NAME="E4:18"/><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon" title="c1">s1</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:18"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T63" title="SCMPDS_4:th.63">SCMPDS_4:63</a></i>;<br/>
<div><i><font color="Green" title="E25">A5</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" title="c5">l</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:18_1"/><i><font color="Green" title="E26">A6</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c5">l</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/><a NAME="E2:18_1"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c5">l</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_5.html#E1:18"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scmpds_5.html#E2:18"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="scmpds_5.html#E3:18"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="scmpds_5.html#T20" target="_self" title="SCMPDS_5:th.20">Th20</a></i>;<br/><b>hence </b><a NAME="E3:18_1"/>
 <a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <font color="Maroon" title="c1">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">l</font>
 <b>by </b><i><a class="txt" href="scmpds_5.html#E4:18"><i><font color="Green" title="E24">A4</font></i></a>, <a class="txt" href="scmpds_5.html#E1:18_1"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="scm_1.html#D2" title="SCM_1:def.2">SCM_1:def 2</a></i>;<br/></div><b>end;</b></div>
<i><font color="Green" title="E26">A7</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:18"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scmpds_5.html#E2:18"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="scmpds_5.html#E3:18"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="scmpds_5.html#T20" target="_self" title="SCMPDS_5:th.20">Th20</a></i>
<br/>.= 
 <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> 
<b>by </b><i><a class="txt" href="scmpds_5.html#E4:18"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="scm_1.html#D2" title="SCM_1:def.2">SCM_1:def 2</a></i>
;<br/>
<a NAME="E7:18"/><i><font color="Green" title="E27">A8</font></i>: 
<font color="Maroon" title="c2">s2</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E2:18"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="scmpds_4.html#T63" title="SCMPDS_4:th.63">SCMPDS_4:63</a></i>;<br/>
<b>hence </b><a NAME="E8:18"/>
 <a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <font color="Maroon" title="c2">s2</font>
 <b>by </b><i><a class="txt" href="scmpds_5.html#E5:18"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="scmpds_5.html#E6:18"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="scm_1.html#D2" title="SCM_1:def.2">SCM_1:def 2</a></i>;<br/>

<a NAME="E9:18"/><b>then </b><i><font color="Green" title="E28">A9</font></i>: 
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <font color="Maroon" title="c1">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E7:18"><i><font color="Green" title="E27">A8</font></i></a>, <a class="ref" href="scmfsa6b.html#T16" title="SCMFSA6B:th.16">SCMFSA6B:16</a></i>;<br/>
<a NAME="E10:18"/>
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <font color="Maroon" title="c1">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E4:18"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="scmfsa6b.html#T16" title="SCMFSA6B:th.16">SCMFSA6B:16</a></i>;<br/>
<b>hence </b><a NAME="E11:18"/>
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c1">s1</font>, <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c2">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_5.html#E1:18"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scmpds_5.html#E2:18"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="scmpds_5.html#E3:18"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="scmpds_5.html#E9:18"><i><font color="Green" title="E28">A9</font></i></a>, <a class="ref" href="scmpds_5.html#T20" target="_self" title="SCMPDS_5:th.20">Th20</a></i>;<br/>


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