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<b>let </b><font color="Maroon" title="c2">s</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="c3">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>let </b><font color="Maroon" title="c4">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/>





<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E11">A1</font></i>: 
not <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c3">I</font>
 ;<br/>

<a NAME="E2:14"/><i><font color="Green" title="E12">A2</font></i>: 
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</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> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1" title="SCMFSA6B:def.1">SCMFSA6B:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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/><b>then reconsider </b><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c4">f</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E3:14_1"/>
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font>
 ;<br/><b>hence </b><a NAME="E4:14_1"/>
contradiction
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T85" title="SCMFSA_2:th.85">SCMFSA_2:85</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:14"/><b>then </b>
not <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</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> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T86" title="RELAT_1:th.86">RELAT_1:86</a></i>;<br/>
<a NAME="E5:14"/><b>then </b><i><font color="Green" title="E13">A3</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E2:14"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/>
<a NAME="E6:14"/><i><font color="Green" title="E14">A4</font></i>: 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">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">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:14"/><b>then </b>
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="ref" href="scm_halt.html#T5" target="_self" title="SCM_HALT:th.5">Th5</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">n</font> being    <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> <b> such that </b><br/><a NAME="E9:14"/><i><font color="Green" title="E15">A5</font></i>: 
(  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c5">n</font> &amp;  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></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>  )
 <b>by </b><i><a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></i>;<br/>
<a NAME="E10:14"/><i><font color="Green" title="E16">A6</font></i>: 
<font color="Maroon" title="c3">I</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E6:14"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="scmfsa6b.html#T8" title="SCMFSA6B:th.8">SCMFSA6B:8</a></i>;<br/>
<a NAME="E11:14"/><i><font color="Green" title="E17">A7</font></i>: 
for <font color="Olive" title="b1">m</font> being   <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>   st <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font> holds <br/> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">I</font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E6:14"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="scm_halt.html#D1" target="_self" title="SCM_HALT:def.1">Def1</a></i>;<br/>
<a NAME="E12:14"/><i><font color="Green" title="E18">A8</font></i>: 
( not <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span> &amp; <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">s</font> )
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T49" title="SCMFSA6A:th.49">SCMFSA6A:49</a>, <a class="ref" href="scmfsa_2.html#T67" title="SCMFSA_2:th.67">SCMFSA_2:67</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c4">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c4">f</font>
<b>by </b><i><a class="txt" href="scm_halt.html#E1:14"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="scm_halt.html#E5:14"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="scm_halt.html#E9:14"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="scm_halt.html#E10:14"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="scm_halt.html#E11:14"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="sf_mastr.html#T71" title="SF_MASTR:th.71">SF_MASTR:71</a></i>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c4">f</font>
<b>by </b><i><a class="txt" href="scm_halt.html#E12:14"><i><font color="Green" title="E18">A8</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
;<br/>


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