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

<b>let </b><font color="Maroon" title="c6">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/>

<a NAME="E1:100"/>
2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Instr-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_2.html#D3" title="AMI_2:def.3">AMI_2:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">loc</font> = 2 as   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  ;<br/>
<b>consider </b><font color="Maroon" title="c8">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <b> such that </b><br/><a NAME="E4:100"/><i><font color="Green" title="E58">A1</font></i>: 
( <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">loc</font> &amp; ( for <font color="Olive" title="b1">d</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  holds  <font color="Maroon" title="c8">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 ) )
 <b>by </b><i><a class="ref" href="scmpds_2.html#T74" target="_self" title="SCMPDS_2:th.74">Th74</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">mj</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E6:100"/><i><font color="Green" title="E59">A2</font></i>: 
( <font color="Maroon" title="c9">mj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">loc</font> &amp;  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c7">loc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c9">mj</font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D19" target="_self" title="SCMPDS_2:def.19">Def19</a></i>;<br/>
<a NAME="E7:100"/><i><font color="Green" title="E60">A3</font></i>: 
<font color="Maroon" title="c7">loc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c8">s</font>
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E4:100"><i><font color="Green" title="E58">A1</font></i></a></i>;<br/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
<b>by </b><i><a class="ref" href="scmpds_2.html#T70" target="_self" title="SCMPDS_2:th.70">Th70</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> 0</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
<b>by </b><i><a class="txt" href="scmpds_2.html#E4:100"><i><font color="Green" title="E58">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">0 <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
<b>by </b><i><a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
<b>by </b><i><a class="ref" href="nat_2.html#T4" title="NAT_2:th.4">NAT_2:4</a></i>
<br/>.= 
<font color="Maroon" title="c9">mj</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:100"><i><font color="Green" title="E59">A2</font></i></a></i>
<br/>.= 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c8">s</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:100"><i><font color="Green" title="E59">A2</font></i></a>, <a class="txt" href="scmpds_2.html#E7:100"><i><font color="Green" title="E60">A3</font></i></a>, <a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a></i>
;<br/>
<b>hence </b><a NAME="E9:100"/>
not  <a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <font color="Maroon" title="c6">a</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T76" target="_self" title="SCMPDS_2:th.76">Th76</a></i>;<br/>


</div>
