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<div class="add">

<b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">s1</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">s2</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="E1:67"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 3 )
 ;<br/>

<a NAME="E2:67"/><i><font color="Green">E39</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 13
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T15">SCMPDS_2:15</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 13 )
 </span><b>by </b><i>, <a class="ref" href="scmpds_5.html#T4" target="_self">Th4</a>, <a class="ref" href="scmpds_3.html#T1">SCMPDS_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_1"><b>suppose </b></a><a NAME="E1:67_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K4">goto</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T35">SCMPDS_2:35</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_1_1"><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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_2"><b>suppose </b></a><a NAME="E1:67_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> <b> such that </b><br/><a NAME="E3:67_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T36">SCMPDS_2:36</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_2_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_2_1_1_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_5.html#E3:67_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_2_1_1_2"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="txt" href="scmpds_5.html#E3:67_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_3"><b>suppose </b></a><a NAME="E1:67_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_3"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T37">SCMPDS_2:37</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_3_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_3_1_1_1"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">k1</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_3_1_1_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_4"><b>suppose </b></a><a NAME="E1:67_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_4"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K8">&lt;&gt;0_goto</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T39">SCMPDS_2:39</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_4_1"><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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_5"><b>suppose </b></a><a NAME="E1:67_1_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_5"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T40">SCMPDS_2:40</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_5_1"><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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_6"><b>suppose </b></a><a NAME="E1:67_1_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_6"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T41">SCMPDS_2:41</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_6_1"><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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_7"><b>suppose </b></a><a NAME="E1:67_1_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_7"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K11">:=</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T42">SCMPDS_2:42</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_7_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_7_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_7_1_1_1"/><i><font color="Green">E92</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:67_1_7_1_1_1"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">k2</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_7_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_7_1_1_2"/><i><font color="Green">E94</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:67_1_7_1_1_2"/><b>then </b><i><font color="Green">E129</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_8"><b>suppose </b></a><a NAME="E1:67_1_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_8"/><i><font color="Green">E142</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K12">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T43">SCMPDS_2:43</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_8_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_8_1_1_1"/><i><font color="Green">E143</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:67_1_8_1_1_1"/><b>then </b><i><font color="Green">E144</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k2</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k2</font>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_8_1_1_2"/><i><font color="Green">E145</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:67_1_8_1_1_2"/><b>then </b><i><font color="Green">E146</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_9"><b>suppose </b></a><a NAME="E1:67_1_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">b</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_9"/><i><font color="Green">E147</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K13">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">b</font>,<font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T44">SCMPDS_2:44</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_9_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_9_1_1_1"/><i><font color="Green">E148</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_9_1_1_1"/><b>then </b><i><font color="Green">E149</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_9_1_1_2"/><i><font color="Green">E150</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_9_1_1_2"/><b>then </b><i><font color="Green">E151</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_10"><b>suppose </b></a><a NAME="E1:67_1_10"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">b</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_10"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K14">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">b</font>,<font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T45">SCMPDS_2:45</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_10_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_10_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_10_1_1_1"/><i><font color="Green">E153</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_10_1_1_1"/><b>then </b><i><font color="Green">E154</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_10_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_10_1_1_2"/><i><font color="Green">E155</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_10_1_1_2"/><b>then </b><i><font color="Green">E156</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_11"><b>suppose </b></a><a NAME="E1:67_1_11"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">b</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_11"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K15">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">b</font>,<font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T46">SCMPDS_2:46</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_11_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_11_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_11_1_1_1"/><i><font color="Green">E158</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_11_1_1_1"/><b>then </b><i><font color="Green">E159</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_11_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_11_1_1_2"/><i><font color="Green">E160</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_11_1_1_2"/><b>then </b><i><font color="Green">E161</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_12"><b>suppose </b></a><a NAME="E1:67_1_12"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">b</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_12"/><i><font color="Green">E162</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K16">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">b</font>,<font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T47">SCMPDS_2:47</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_12_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_12_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_12_1_1_1"/><i><font color="Green">E163</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_12_1_1_1"/><b>then </b><i><font color="Green">E164</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_12_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_12_1_1_2"/><i><font color="Green">E165</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_12_1_1_2"/><b>then </b><i><font color="Green">E166</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <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"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_12_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_12_1_1_2_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_12_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_12_1_1_2_1_1_1"/><i><font color="Green">E167</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_12_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E168</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_5.html#T8" target="_self">Th8</a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_5.html#T9" target="_self">Th9</a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_12_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_12_1_1_2_1_1_2"/><i><font color="Green">E169</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_12_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E170</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_5.html#T8" target="_self">Th8</a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_5.html#T9" target="_self">Th9</a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_13"><b>suppose </b></a><a NAME="E1:67_1_13"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 13
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">b</font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">k1</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:67_1_13"/><i><font color="Green">E171</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K17">:=</a> <font color="Maroon">b</font>,<font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T48">SCMPDS_2:48</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_1_13_1_1"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_13_1_1_1"><b>suppose </b></a><a NAME="E1:67_1_13_1_1_1"/><i><font color="Green">E172</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_13_1_1_1"/><b>then </b><i><font color="Green">E173</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">k2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#T3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_13_1_1_2"><b>suppose </b></a><a NAME="E1:67_1_13_1_1_2"/><i><font color="Green">E174</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:67_1_13_1_1_2"/><b>then </b><i><font color="Green">E175</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_5.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:67_1_13"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></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"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font></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>end;</b></div></div><b>end;</b></div>

</div>
