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<b>let </b><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>assume </b><a NAME="E1:45"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="scmpds_6.html#R1" target="_self">is_closed_on</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="scmpds_6.html#R2" target="_self">is_halting_on</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:45"/><i><font color="Green">E41</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E3:45"/>
<font color="Maroon">c<sub>3</sub></font> <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> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E4:45"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:45"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/>
<a NAME="E6:45"/><i><font color="Green">E43</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">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_6.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_6.html#T40" target="_self">Th40</a></i>;<br/>
 <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">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></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">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</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">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</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">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_6.html#E5:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmpds_6.html#E6:45"><i><font color="Green">E43</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/>
<b>hence </b><a NAME="E8:45"/>
 <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">c<sub>4</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></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#E6:45"><i><font color="Green">E43</font></i></a>, <a class="ref" href="scmpds_5.html#D3">SCMPDS_5:def 3</a></i>;<br/>


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