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<b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c4">I</font> be  <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="c5">J</font> be   <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/>





<b>set </b><font color="Maroon" title="c6">m</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/>
<b>set </b><font color="Maroon" title="c7">G</font> =  <a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">s2</font> = <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:51"/><i><font color="Green" title="E45">A1</font></i>: 
( <font color="Maroon" title="c4">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c3">s</font> &amp; <font color="Maroon" title="c4">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c3">s</font> )
 ;<br/>

<a NAME="E2:51"/><b>then </b>
( <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> &amp;  <a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p0">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></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#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E48"><i><font color="Green" title="E40">Lm2</font></i></a></i>;<br/>
<b>then </b> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <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="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</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> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_6.html#E1:51"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="scmpds_6.html#E48"><i><font color="Green" title="E40">Lm2</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E4:51"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_5.html#T22" title="SCMPDS_5:th.22">SCMPDS_5:22</a></i>;<br/>


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