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<b>let </b><font color="Maroon" title="c1">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c2">I</font> be  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a> <a href="scmpds_5.html#V3" title="SCMPDS_5:attr.3">No-StopCode</a> <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/><b>let </b><font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/>





<b>set </b><font color="Maroon" title="c4">sI</font> = <font color="Maroon" title="c1">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">s1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">k</font>;<br/>
<b>set </b><font color="Maroon" title="c6">s2</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font>;<br/>
<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E32">A1</font></i>: 
(  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">s</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K30" title="AMI_1:func.30">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:50"/><b>then </b><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a>, <a class="ref" href="scmpds_4.html#T57" title="SCMPDS_4:th.57">SCMPDS_4:57</a></i>;<br/>
<a NAME="E3:50"/><i><font color="Green" title="E34">A3</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">I</font>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:50"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="scmpds_5.html#T28" target="_self" title="SCMPDS_5:th.28">Th28</a></i>;<br/>
 <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">s</font>,<font color="Maroon" title="c3">k</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:50"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="scmpds_5.html#T29" target="_self" title="SCMPDS_5:th.29">Th29</a>, <a class="ref" href="ami_1.html#T121" title="AMI_1:th.121">AMI_1:121</a></i>
<br/>.= 
<font color="Maroon" title="c2">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_5.html#E2:50"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="scmpds_5.html#E3:50"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
;<br/>
<b>hence </b><a NAME="E5:50"/>
 <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">s</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_5.html#E3:50"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="scmpds_5.html#D3" target="_self" title="SCMPDS_5:def.3">Def3</a></i>;<br/>


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