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<b>let </b><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c4">I</font> be  <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a> <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E18">A2</font></i>: 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font>
 <b>and </b><br/><a NAME="E3:22"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ;<br/>

<a NAME="E4:22"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c2">s1</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E1:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="scm_halt.html#T5" target="_self" title="SCM_HALT:th.5">Th5</a></i>;<br/>
<div><i><font color="Green" title="E21">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_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="E1:22_1"/><i><font color="Green" title="E22">A6</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="c3">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ;<br/><a NAME="E2:22_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="c2">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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#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">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c5">l</font></span>)</span>
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scm_halt.html#E2:22"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scm_halt.html#E3:22"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="scm_halt.html#T14" target="_self" title="SCM_HALT:th.14">Th14</a></i>;<br/><b>hence </b><a NAME="E3:22_1"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c2">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="scm_halt.html#E4:22"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="scm_halt.html#E1:22_1"><i><font color="Green" title="E22">A6</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="E22">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="c3">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="c2">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="c2">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="c2">s1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scm_halt.html#E1:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scm_halt.html#E2:22"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scm_halt.html#E3:22"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="scm_halt.html#T14" target="_self" title="SCM_HALT:th.14">Th14</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="txt" href="scm_halt.html#E4:22"><i><font color="Green" title="E20">A4</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="E7:22"/><i><font color="Green" title="E23">A8</font></i>: 
<font color="Maroon" title="c3">s2</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E2:22"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="scm_halt.html#T5" target="_self" title="SCM_HALT:th.5">Th5</a></i>;<br/>
<b>hence </b><a NAME="E8:22"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <font color="Maroon" title="c2">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="c3">s2</font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E5:22"><i><font color="Green" title="E21">A5</font></i></a>, <a class="txt" href="scm_halt.html#E6:22"><i><font color="Green" title="E22">A7</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="E9:22"/><b>then </b><i><font color="Green" title="E24">A9</font></i>: 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">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="c3">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="c2">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E7:22"><i><font color="Green" title="E23">A8</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>;<br/>
<a NAME="E10:22"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c2">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="c2">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="c2">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E4:22"><i><font color="Green" title="E20">A4</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="E11:22"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c2">s1</font>, <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scm_halt.html#E2:22"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scm_halt.html#E3:22"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="scm_halt.html#E9:22"><i><font color="Green" title="E24">A9</font></i></a>, <a class="ref" href="scm_halt.html#T14" target="_self" title="SCM_HALT:th.14">Th14</a></i>;<br/>


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