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<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="scmpds_2.html#M1" target="_self">Int_position</a> ;<br/>

<a NAME="E1:100"/>
2 <a href="nat_1.html#K2">*</a> 1 <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_2.html#D3">AMI_2:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = 2 as   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1" target="_self">SCMPDS</a>  ;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> <b> such that </b><br/><a NAME="E4:100"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmpds_2.html#M1" target="_self">Int_position</a>  holds <font color="Maroon">c<sub>8</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 ) )
 <b>by </b><i><a class="ref" href="scmpds_2.html#T74" target="_self">Th74</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E6:100"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="scmpds_2.html#K18" target="_self">Next</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K15">Next</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D19" target="_self">Def19</a></i>;<br/>
<a NAME="E7:100"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E4:100"><i><font color="Green">E58</font></i></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#K5" target="_self">return</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>8</sub></font></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" target="_self">SCMPDS</a> </span>)</span> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3" target="_self">DataLoc</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="scmpds_1.html#K23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="ref" href="scmpds_2.html#T70" target="_self">Th70</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> 0</span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="txt" href="scmpds_2.html#E4:100"><i><font color="Green">E58</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="ref" href="nat_2.html#T4">NAT_2:4</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:100"><i><font color="Green">E59</font></i></a></i>
<br/>.= 
 <a href="scmpds_2.html#K18" target="_self">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:100"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmpds_2.html#E7:100"><i><font color="Green">E60</font></i></a>, <a class="ref" href="ami_2.html#D15">AMI_2:def 15</a></i>
;<br/>
<b>hence </b><a NAME="E9:100"/>
not  <a href="scmpds_2.html#K5" target="_self">return</a> <font color="Maroon">c<sub>6</sub></font> is <a href="ami_1.html#V3">halting</a>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T76" target="_self">Th76</a></i>;<br/>


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