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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#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">s1</font> &amp;  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s2</font> &amp; <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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/>(  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c2">s2</font> &amp;  <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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><b>let </b><font color="Maroon" title="c3">I</font> be  <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">s1</font> &amp;  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s2</font> &amp; <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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  implies (  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c2">s2</font> &amp;  <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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ) )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:10"/><i><font color="Green" title="E6">A1</font></i>: 
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">s1</font>
 <b>and </b><br/><a NAME="E2:10"/><i><font color="Green" title="E7">A2</font></i>: 
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s2</font>
 <b>and </b><br/><a NAME="E3:10"/><i><font color="Green" title="E8">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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c2">s2</font> &amp;  <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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/>

<a NAME="E4:10"/><i><font color="Green" title="E9">A4</font></i>: 
<font color="Maroon" title="c1">s1</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmisort.html#E1:10"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="scm_halt.html#T5" title="SCM_HALT:th.5">SCM_HALT:5</a></i>;<br/>
<div><i><font color="Green" title="E10">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">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>  implies  <a href="ami_1.html#K31" title="AMI_1:func.31">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="c4">l</font> )</span><br/><b>assume </b><a NAME="E1:10_1"/><i><font color="Green" title="E11">A6</font></i>: 
 <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> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K31" title="AMI_1:func.31">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="c4">l</font></span><br/><a NAME="E2:10_1"/>
 <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> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c4">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">l</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:10"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="scmisort.html#E2:10"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="scmisort.html#E3:10"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="scmisort.html#T11" target="_self" title="SCMISORT:th.11">Th11</a></i>;<br/><b>hence </b><a NAME="E3:10_1"/>
 <a href="ami_1.html#K31" title="AMI_1:func.31">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="c4">l</font>
 <b>by </b><i><a class="txt" href="scmisort.html#E4:10"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="scmisort.html#E1:10_1"><i><font color="Green" title="E11">A6</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<i><font color="Green" title="E11">A7</font></i>:  <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> <font color="Maroon" title="c2">s2</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:10"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="scmisort.html#E2:10"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="scmisort.html#E3:10"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="scmisort.html#T11" target="_self" title="SCMISORT:th.11">Th11</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="scmisort.html#E4:10"><i><font color="Green" title="E9">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="E7:10"/>
<font color="Maroon" title="c2">s2</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmisort.html#E2:10"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="scm_halt.html#T5" title="SCM_HALT:th.5">SCM_HALT:5</a></i>;<br/>
<b>hence </b><a NAME="E8:10"/>
 <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c2">s2</font>
 <b>by </b><i><a class="txt" href="scmisort.html#E5:10"><i><font color="Green" title="E10">A5</font></i></a>, <a class="txt" href="scmisort.html#E6:10"><i><font color="Green" title="E11">A7</font></i></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><br/>

<a NAME="E9:10"/><b>then </b><i><font color="Green" title="E12">A8</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>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c1">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmisort.html#E2:10"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a>, <a class="ref" href="scm_halt.html#T5" title="SCM_HALT:th.5">SCM_HALT:5</a></i>;<br/>
<a NAME="E10:10"/>
 <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>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c1">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmisort.html#E1:10"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a>, <a class="ref" href="scm_halt.html#T5" title="SCM_HALT:th.5">SCM_HALT:5</a></i>;<br/>
<b>hence </b><a NAME="E11:10"/>
 <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>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="scmisort.html#E1:10"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="scmisort.html#E2:10"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="scmisort.html#E3:10"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="scmisort.html#E9:10"><i><font color="Green" title="E12">A8</font></i></a>, <a class="ref" href="scmisort.html#T11" target="_self" title="SCMISORT:th.11">Th11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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