<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">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="c5">I</font> be   <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/>





<b>set </b><font color="Maroon" title="c6">iI</font> =  <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="c5">I</font></span>)</span>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:27"/><i><font color="Green" title="E20">A1</font></i>: 
( <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c3">s1</font> )
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green" title="E21">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="c5">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font>
 <b>and </b><br/><a NAME="E3:27"/><i><font color="Green" title="E22">A3</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="c5">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font>
 <b>and </b><br/><a NAME="E4:27"/><i><font color="Green" title="E23">A4</font></i>: 
<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">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="E5:27"/>
<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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="c5">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/>
<a NAME="E6:27"/><b>then </b><i><font color="Green" title="E24">A5</font></i>: 
<font color="Maroon" title="c3">s1</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></i>;<br/>
<div><i><font color="Green" title="E25">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">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="E1:27_1"/><i><font color="Green" title="E26">A7</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c7">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="E2:27_1"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c7">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c7">l</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="scmpds_7.html#T26" target="_self" title="SCMPDS_7:th.26">Th26</a></i>;<br/><b>hence </b><a NAME="E3:27_1"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">l</font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E6:27"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="scmpds_7.html#E1:27_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/></div><b>end;</b></div>
<i><font color="Green" title="E26">A8</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c3">s1</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c3">s1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="scmpds_7.html#T26" target="_self" title="SCMPDS_7:th.26">Th26</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_7.html#E6:27"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>
;<br/>
<a NAME="E9:27"/><i><font color="Green" title="E27">A9</font></i>: 
<font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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="c5">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/>
<a NAME="E10:27"/>
<font color="Maroon" title="c3">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="scmpds_6.html#T4" title="SCMPDS_6:th.4">SCMPDS_6:4</a></i>;<br/>
<a NAME="E11:27"/><b>then </b>
<font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s2</font>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="scmpds_6.html#T37" title="SCMPDS_6:th.37">SCMPDS_6:37</a></i>;<br/>
<a NAME="E12:27"/><b>then </b><i><font color="Green" title="E28">A10</font></i>: 
<font color="Maroon" title="c4">s2</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E9:27"><i><font color="Green" title="E27">A9</font></i></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></i>;<br/>
<b>hence </b><a NAME="E13:27"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c4">s2</font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E7:27"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="scmpds_7.html#E8:27"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>;<br/>

<a NAME="E14:27"/><b>then </b><i><font color="Green" title="E29">A11</font></i>: 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c3">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E12:27"><i><font color="Green" title="E28">A10</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>;<br/>
<a NAME="E15:27"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c3">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E6:27"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>;<br/>
<b>hence </b><a NAME="E16:27"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">s1</font>, <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c4">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_7.html#E1:27"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="scmpds_7.html#E14:27"><i><font color="Green" title="E29">A11</font></i></a>, <a class="ref" href="scmpds_7.html#T26" target="_self" title="SCMPDS_7:th.26">Th26</a></i>;<br/>


</div>
