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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>, <font color="Maroon" title="c4">J</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="c5">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/>





<a NAME="E1:79"/><i><font color="Green" title="E56">A1</font></i>: 
 <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c4">J</font>,<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c3">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8b.html#D3" title="SCMFSA8B:def.3">SCMFSA8B:def 3</a></i>;<br/>
<a NAME="E2:79"/>
 <a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c3">I</font> is <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>
 
<b>by </b><i><a class="ref" href="scm_halt.html#T53" target="_self" title="SCM_HALT:th.53">Th53</a></i>;<br/>
<b>hence </b><a NAME="E3:79"/>
 <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font> is <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:79"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="scm_halt.html#T47" target="_self" title="SCM_HALT:th.47">Th47</a></i>;<br/>

<a NAME="E4:79"/><i><font color="Green" title="E57">A2</font></i>: 
( <font color="Maroon" title="c3">I</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c2">s</font> &amp; <font color="Maroon" title="c3">I</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c2">s</font> )
 
<b>by </b><i><a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th35</a>, <a class="ref" href="scm_halt.html#T36" target="_self" title="SCM_HALT:th.36">Th36</a></i>;<br/>
<a NAME="E5:79"/><i><font color="Green" title="E58">A3</font></i>: 
( <font color="Maroon" title="c4">J</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c2">s</font> &amp; <font color="Maroon" title="c4">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c2">s</font> )
 
<b>by </b><i><a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th35</a>, <a class="ref" href="scm_halt.html#T36" target="_self" title="SCM_HALT:th.36">Th36</a></i>;<br/>
<b>thus </b><a NAME="E6:79"/>
( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c5">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 implies  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font></span>)</span>,<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="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="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 7</span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="scm_halt.html#E4:79"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="scm_halt.html#T55" target="_self" title="SCM_HALT:th.55">Th55</a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:79_1"/><i><font color="Green" title="E59">A4</font></i>: 
<font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c5">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:79_1_1"/>
( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1_1_1"><b>suppose </b></a><a NAME="E1:79_1_1_1"/>
<font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:79_1_1_1"/>
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font></span>)</span>,<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="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 7</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scm_halt.html#E5:79"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="scm_halt.html#T56" target="_self" title="SCM_HALT:th.56">Th56</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1_1_2"><b>suppose </b></a><a NAME="E1:79_1_1_2"/>
<font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:79_1_1_2"/>
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font></span>)</span>,<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="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 7</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scm_halt.html#E5:79"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="scm_halt.html#E1:79_1"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="scm_halt.html#T57" target="_self" title="SCM_HALT:th.57">Th57</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>


</div>
