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<b>let </b><font color="Maroon" title="c1">I</font> be  <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a> <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="c2">a</font> be  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>  <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E20">A1</font></i>: 
for <font color="Olive" title="b1">s</font> being  <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>   holds <br/>( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> or <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">t</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>assume </b><a NAME="E1:30_1"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c3">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_1_1"/>
( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">t</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> or <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">t</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 )
 </span><b>by </b><i><a class="txt" href="scmisort.html#E1:30"><i><font color="Green" title="E20">A1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1"><b>suppose </b></a><a NAME="E1:30_1_1_1"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">t</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">t</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_2"><b>suppose </b></a><a NAME="E1:30_1_1_2"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">t</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_2"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" title="SCMFSA6B:func.3">IExec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">t</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:30_1"><i><font color="Green" title="E21">A2</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:30"/>
 <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font> is <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>
 <b>by </b><i><a class="ref" href="scmisort.html#T29" target="_self" title="SCMISORT:th.29">Th29</a></i>;<br/>


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