<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">I</font> be  <a href="scmpds_5.html#V3">No-StopCode</a> <a href="scmpds_4.html#NM1">Program-block</a>;<br/><b>let </b><font color="Maroon">J</font> be   <a href="scmpds_4.html#NM1">Program-block</a>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">I</font> <a href="scmpds_6.html#R1" target="_self">is_closed_on</a> <font color="Maroon">s</font>
 ;<br/>

<b>assume </b><a NAME="E2:47"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">I</font> <a href="scmpds_6.html#R2" target="_self">is_halting_on</a> <font color="Maroon">s</font>
 ;<br/>

<b>set </b><font color="Maroon">G1</font> =  <a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">SS</font> =  <a href="scmpds_3.html#K5">SCMPDS-Stop</a> ;<br/>
<b>set </b><font color="Maroon">J2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> ;<br/>
<b>set </b><font color="Maroon">IJ</font> = <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font>;<br/>
<b>set </b><font color="Maroon">pJ</font> =  <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">IsJ</font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">s1</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">s2</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>;<br/>
<i><font color="Green">E45</font></i>:  <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> 
<b>by </b><i><a class="ref" href="scmpds_4.html#D7">SCMPDS_4:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> 
<b>by </b><i><a class="ref" href="scmpds_4.html#T46">SCMPDS_4:46</a></i>
<br/>.= 
<font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T46">SCMPDS_4:46</a></i>
;<br/>
<a NAME="E4:47"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T46">SCMPDS_4:46</a></i>;<br/>
<i><font color="Green">E47</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E6:47"/>
 <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T9">SCMPDS_4:9</a></i>;<br/>
<a NAME="E7:47"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E8:47"/><i><font color="Green">E49</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>;<br/>
<i><font color="Green">E50</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T46">SCMPDS_4:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E10:47"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E11:47"/><b>then </b><i><font color="Green">E102</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span>
 
;<br/>
<a NAME="E12:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E7:47"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E13:47"/><b>then </b><i><font color="Green">E103</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<a NAME="E14:47"/><i><font color="Green">E104</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E9:47"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<a NAME="E15:47"/><i><font color="Green">E105</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<i><font color="Green">E106</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T46">SCMPDS_4:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T37">SCMPDS_4:37</a></i>
<br/>.= 
 <a href="scmpds_2.html#K4">goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i/>
;<br/>
<b>set </b><font color="Maroon">sm</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E17:47"/><i><font color="Green">E107</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E2:47"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmpds_6.html#T3" target="_self">Th3</a>, <a class="txt" href="scmpds_6.html#E3:47"><i><font color="Green">E45</font></i></a>, </i>;<br/>
<a NAME="E18:47"/><b>then </b><i><font color="Green">E108</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E2:47"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmpds_6.html#T3" target="_self">Th3</a>, </i>;<br/>
<b>then </b><i><font color="Green">E109</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_6.html#E5:47"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmpds_6.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_6.html#T4" target="_self">Th4</a>, <a class="ref" href="scmpds_4.html#T33">SCMPDS_4:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span> <a href="scmpds_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
<br/>.= 
 <a href="scmpds_2.html#K4">goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_6.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_4.html#T38">SCMPDS_4:38</a></i>
;<br/>
<i><font color="Green">E110</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span> = 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_6.html#E8:47"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span>

;<br/>
<a NAME="E21:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a>, <a class="ref" href="scmpds_4.html#T74">SCMPDS_4:74</a></i>;<br/>
<a NAME="E22:47"/><b>then </b><i><font color="Green">E111</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<a NAME="E23:47"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E7:47"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmpds_6.html#T10" target="_self">Th10</a>, <a class="ref" href="scmpds_4.html#T74">SCMPDS_4:74</a></i>;<br/>
<a NAME="E24:47"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E25:47"/><b>then </b><i><font color="Green">E112</font></i>: 
 <a href="scmpds_3.html#K2">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#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<i><font color="Green">E113</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_6.html#E4:47"><i><font color="Green">E46</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span> <a href="scmpds_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="ref" href="scmpds_4.html#T38">SCMPDS_4:38</a>, <a class="ref" href="scmpds_4.html#T73">SCMPDS_4:73</a></i>
;<br/>
<b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_6.html#T8" target="_self">Th8</a>, </i>
<br/>.= 
 <a href="scmpds_3.html#K2">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#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/>

<b>then </b><i><font color="Green">E114</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_6.html#E5:47"><i><font color="Green">E47</font></i></a>, , <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmpds_4.html#T33">SCMPDS_4:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="ref" href="scmpds_6.html#T12" target="_self">Th12</a>, , <a class="ref" href="scmpds_4.html#T38">SCMPDS_4:38</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E30:47"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:47_11"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_11_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_11_1"/>
( <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> or  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_11_1_1"><b>suppose </b></a><a NAME="E1:47_11_1_1"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:47_11_1_1"/><b>then </b>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_6.html#E2:47"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmpds_6.html#T3" target="_self">Th3</a>, <a class="ref" href="scmpds_6.html#T2" target="_self">Th2</a></i>;<br/><b>hence </b><a NAME="E3:47_11_1_1"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_6.html#E2:47"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmpds_6.html#T3" target="_self">Th3</a>, <a class="txt" href="scmpds_6.html#E3:47"><i><font color="Green">E45</font></i></a>, , <a class="ref" href="scmpds_6.html#T1" target="_self">Th1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_11_1_2"><b>suppose </b></a><a NAME="E1:47_11_1_2"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 ;<br/><div class="add"><a NAME="E2:47_11_1_2"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_6.html#T14" target="_self">Th14</a>, <a class="ref" href="xreal_1.html#T1">XREAL_1:1</a></i>;<br/><b>hence </b><a NAME="E3:47_11_1_2"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="scmpds_6.html#T9" target="_self">Th9</a>, <a class="ref" href="scmpds_2.html#T85">SCMPDS_2:85</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<div><i><font color="Green">E118</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_12"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:47_12"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><a NAME="E2:47_12"/><b>then </b>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:47_12"/>
<span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E33:47"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_6.html#E2:47"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmpds_6.html#T3" target="_self">Th3</a>, , </i>;<br/>

<b>thus </b><a NAME="E34:47"/>
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i>, <a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/>

<b>hence </b><a NAME="E35:47"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="scmpds_6.html#T14" target="_self">Th14</a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>


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