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

<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</font> be   <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> ;<br/><b>let </b><font color="Maroon" title="c3">n</font>, <font color="Maroon" title="c4">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c5">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:107"/><i><font color="Green" title="E57">A1</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c4">m</font>
 <b>and </b><br/><a NAME="E2:107"/><i><font color="Green" title="E58">A2</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="scmpds_4.html#R1" title="SCMPDS_4:pred.1">valid_at</a> <font color="Maroon" title="c4">m</font>
 <b>and </b><br/><a NAME="E3:107"/><i><font color="Green" title="E59">A3</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:107"/><i><font color="Green" title="E60">A4</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3
 <b>and </b><br/><a NAME="E5:107"/><i><font color="Green" title="E61">A5</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</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="c2">s2</font>
 <b>and </b><br/><a NAME="E6:107"/><i><font color="Green" title="E62">A6</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 ;<br/>

<b>set </b><font color="Maroon" title="c6">D</font> =  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> ;<br/>
<b>consider </b><font color="Maroon" title="c7">k1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E8:107"/><i><font color="Green" title="E63">A7</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c7">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T32" title="SCMPDS_3:th.32">SCMPDS_3:32</a></i>;<br/>
<a NAME="E9:107"/><i><font color="Green" title="E64">A8</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">s2</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> = 
<span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E8:107"><i><font color="Green" title="E63">A7</font></i></a>, <a class="ref" href="scmpds_4.html#T70" target="_self" title="SCMPDS_4:th.70">Th70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D3" title="SCMPDS_3:def.3">SCMPDS_3:def 3</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T70" target="_self" title="SCMPDS_4:th.70">Th70</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="c2">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green" title="E61">A5</font></i></a>, <a class="txt" href="scmpds_4.html#E8:107"><i><font color="Green" title="E63">A7</font></i></a>, <a class="ref" href="scmpds_3.html#D3" title="SCMPDS_3:def.3">SCMPDS_3:def 3</a></i>
;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon" title="c8">Ci</font> =  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font>;<br/>
<div><i><font color="Green" title="E65">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:107_2"/>
(  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 &amp;  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp;  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 &amp;  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 5 &amp;  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 6 )
 ;<br/><a NAME="E2:107_2"/><b>then </b><i><font color="Green" title="E66">A10</font></i>: 
not  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">0,1,4,5,6</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E3:107_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107_2"><i><font color="Green" title="E66">A10</font></i></a>, <a class="ref" href="scmpds_4.html#T6" target="_self" title="SCMPDS_4:th.6">Th6</a></i>;<br/><b>hence </b><a NAME="E4:107_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green" title="E64">A8</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_2"><i><font color="Green" title="E66">A10</font></i></a>, <a class="ref" href="scmpds_4.html#T6" target="_self" title="SCMPDS_4:th.6">Th6</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E66">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>let </b><font color="Maroon" title="c10">k1</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/><b>thus </b><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E12:107"/><i><font color="Green" title="E67">A12</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 13
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T15" title="SCMPDS_2:th.15">SCMPDS_2:15</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4"/>
(  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 )
 </span><b>by </b><i><a class="txt" href="scmpds_4.html#E3:107"><i><font color="Green" title="E59">A3</font></i></a>, <a class="txt" href="scmpds_4.html#E4:107"><i><font color="Green" title="E60">A4</font></i></a>, <a class="txt" href="scmpds_4.html#E12:107"><i><font color="Green" title="E67">A12</font></i></a>, <a class="ref" href="scmpds_3.html#T1" title="SCMPDS_3:th.1">SCMPDS_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_1"><b>suppose </b></a><a NAME="E1:107_4_1"/>
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_1"/><i><font color="Green" title="E68">A13</font></i>: 
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <font color="Maroon" title="c9">k1</font> &amp; <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c9">k1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self" title="SCMPDS_4:def.11">Def11</a></i>;<br/><div><i><font color="Green" title="E69">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">a</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green" title="E68">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green" title="E68">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/></div><b>end;</b></div><a NAME="E5:107_4_1"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c9">k1</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green" title="E68">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> = 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c9">k1</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green" title="E61">A5</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green" title="E68">A13</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self" title="SCMPDS_4:th.82">Th82</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green" title="E68">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><br/><b>thus </b><a NAME="E7:107_4_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_1"><i><font color="Green" title="E69">A14</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_2"><b>suppose </b></a><a NAME="E1:107_4_2"/><i><font color="Green" title="E68">A15</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c10">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_2"/><i><font color="Green" title="E69">A16</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c10">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T37" title="SCMPDS_2:th.37">SCMPDS_2:37</a></i>;<br/><div><i><font color="Green" title="E70">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_2_1_1"/>
( <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b</font> or <font color="Maroon" title="c9">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_2_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_2_1_1_1"/><i><font color="Green" title="E71">A18</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c11">b</font> = 
<font color="Maroon" title="c10">k1</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green" title="E69">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c11">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green" title="E69">A16</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_2_1_1_1"><i><font color="Green" title="E71">A18</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_2_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_2_1_1_2"/><i><font color="Green" title="E71">A19</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c11">b</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c11">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green" title="E69">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c11">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c11">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green" title="E69">A16</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_2_1_1_2"><i><font color="Green" title="E71">A19</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_2"><i><font color="Green" title="E68">A15</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_2"><i><font color="Green" title="E70">A17</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_3"><b>suppose </b></a><a NAME="E1:107_4_3"/>
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c10">k1</font>, <font color="Maroon" title="c11">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_3"/><i><font color="Green" title="E68">A20</font></i>: 
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Maroon" title="c11">k2</font> &amp; <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">k2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self" title="SCMPDS_4:def.11">Def11</a></i>;<br/><div><i><font color="Green" title="E69">A21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green" title="E68">A20</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green" title="E68">A20</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
;<br/></div><b>end;</b></div><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_3_2_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 or <font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_3_2_1_1"><b>suppose </b></a><a NAME="E1:107_4_3_2_1_1"/><i><font color="Green" title="E70">A22</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_3_2_1_1"/><b>then </b><i><font color="Green" title="E71">A23</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>;<br/><a NAME="E3:107_4_3_2_1_1"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c11">k2</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green" title="E68">A20</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_3_2_1_1"><i><font color="Green" title="E70">A22</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> = 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c11">k2</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green" title="E61">A5</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green" title="E68">A20</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self" title="SCMPDS_4:th.82">Th82</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green" title="E68">A20</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_3_2_1_1"><i><font color="Green" title="E71">A23</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_3_2_1_2"><b>suppose </b></a><a NAME="E1:107_4_3_2_1_2"/><i><font color="Green" title="E70">A24</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_3_2_1_2"/><b>then </b><i><font color="Green" title="E71">A25</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>;<br/><a NAME="E3:107_4_3_2_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green" title="E68">A20</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_3_2_1_2"><i><font color="Green" title="E70">A24</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>;<br/><b>hence </b><a NAME="E4:107_4_3_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green" title="E64">A8</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green" title="E68">A20</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_3_2_1_2"><i><font color="Green" title="E71">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><b>thus </b><a NAME="E6:107_4_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_3"><i><font color="Green" title="E69">A21</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_4"><b>suppose </b></a><a NAME="E1:107_4_4"/>
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c10">k1</font>, <font color="Maroon" title="c11">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_4"/><i><font color="Green" title="E68">A26</font></i>: 
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c11">k2</font> &amp; <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">k2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self" title="SCMPDS_4:def.11">Def11</a></i>;<br/><div><i><font color="Green" title="E69">A27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green" title="E68">A26</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green" title="E68">A26</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
;<br/></div><b>end;</b></div><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_4_2_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 or <font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_4_2_1_1"><b>suppose </b></a><a NAME="E1:107_4_4_2_1_1"/><i><font color="Green" title="E70">A28</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_4_2_1_1"/><b>then </b><i><font color="Green" title="E71">A29</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>;<br/><a NAME="E3:107_4_4_2_1_1"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c11">k2</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green" title="E68">A26</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_4_2_1_1"><i><font color="Green" title="E70">A28</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> = 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c11">k2</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green" title="E61">A5</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green" title="E68">A26</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self" title="SCMPDS_4:th.82">Th82</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green" title="E68">A26</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_4_2_1_1"><i><font color="Green" title="E71">A29</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_4_2_1_2"><b>suppose </b></a><a NAME="E1:107_4_4_2_1_2"/><i><font color="Green" title="E70">A30</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_4_2_1_2"/><b>then </b><i><font color="Green" title="E71">A31</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>;<br/><a NAME="E3:107_4_4_2_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green" title="E68">A26</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_4_2_1_2"><i><font color="Green" title="E70">A30</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/><b>hence </b><a NAME="E4:107_4_4_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green" title="E64">A8</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green" title="E68">A26</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_4_2_1_2"><i><font color="Green" title="E71">A31</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><b>thus </b><a NAME="E6:107_4_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_4"><i><font color="Green" title="E69">A27</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_5"><b>suppose </b></a><a NAME="E1:107_4_5"/>
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c10">k1</font>, <font color="Maroon" title="c11">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_5"/><i><font color="Green" title="E68">A32</font></i>: 
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <font color="Maroon" title="c11">k2</font> &amp; <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">k2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self" title="SCMPDS_4:def.11">Def11</a></i>;<br/><div><i><font color="Green" title="E69">A33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green" title="E68">A32</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green" title="E68">A32</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/></div><b>end;</b></div><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_5_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_5_2_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 or <font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_5_2_1_1"><b>suppose </b></a><a NAME="E1:107_4_5_2_1_1"/><i><font color="Green" title="E70">A34</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_5_2_1_1"/><b>then </b><i><font color="Green" title="E71">A35</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>;<br/><a NAME="E3:107_4_5_2_1_1"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c11">k2</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green" title="E68">A32</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_5_2_1_1"><i><font color="Green" title="E70">A34</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> = 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c11">k2</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green" title="E61">A5</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green" title="E68">A32</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self" title="SCMPDS_4:th.82">Th82</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green" title="E68">A32</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_5_2_1_1"><i><font color="Green" title="E71">A35</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_5_2_1_2"><b>suppose </b></a><a NAME="E1:107_4_5_2_1_2"/><i><font color="Green" title="E70">A36</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_5_2_1_2"/><b>then </b><i><font color="Green" title="E71">A37</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>;<br/><a NAME="E3:107_4_5_2_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green" title="E68">A32</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_5_2_1_2"><i><font color="Green" title="E70">A36</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>;<br/><b>hence </b><a NAME="E4:107_4_5_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green" title="E64">A8</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green" title="E68">A32</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_5_2_1_2"><i><font color="Green" title="E71">A37</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><b>thus </b><a NAME="E6:107_4_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_5"><i><font color="Green" title="E69">A33</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_6"><b>suppose </b></a><a NAME="E1:107_4_6"/><i><font color="Green" title="E68">A38</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c10">k1</font>, <font color="Maroon" title="c11">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_6"/><i><font color="Green" title="E69">A39</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">k1</font> <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Maroon" title="c11">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T42" title="SCMPDS_2:th.42">SCMPDS_2:42</a></i>;<br/><div><i><font color="Green" title="E70">A40</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_6_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_6_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_6_1_1_1"/><i><font color="Green" title="E71">A41</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 ;<br/><div class="add"><a NAME="E2:107_4_6_1_1_1"/><b>then </b><i><font color="Green" title="E72">A42</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font> = 
<font color="Maroon" title="c11">k2</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green" title="E69">A39</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_6_1_1_1"><i><font color="Green" title="E71">A41</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green" title="E69">A39</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_6_1_1_1"><i><font color="Green" title="E72">A42</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_6_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_6_1_1_2"/><i><font color="Green" title="E71">A43</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 ;<br/><div class="add"><a NAME="E2:107_4_6_1_1_2"/><b>then </b><i><font color="Green" title="E72">A44</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green" title="E69">A39</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_6_1_1_2"><i><font color="Green" title="E71">A43</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green" title="E69">A39</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_6_1_1_2"><i><font color="Green" title="E72">A44</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_6"><i><font color="Green" title="E68">A38</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_6"><i><font color="Green" title="E70">A40</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_7"><b>suppose </b></a><a NAME="E1:107_4_7"/><i><font color="Green" title="E68">A45</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c10">k1</font>, <font color="Maroon" title="c11">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_7"/><i><font color="Green" title="E69">A46</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">k1</font>,<font color="Maroon" title="c11">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T43" title="SCMPDS_2:th.43">SCMPDS_2:43</a></i>;<br/><div><i><font color="Green" title="E70">A47</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_7_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_7_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_7_1_1_1"/><i><font color="Green" title="E71">A48</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 ;<br/><div class="add"><a NAME="E2:107_4_7_1_1_1"/><b>then </b><i><font color="Green" title="E72">A49</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">k2</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green" title="E69">A46</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_7_1_1_1"><i><font color="Green" title="E71">A48</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">k2</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green" title="E69">A46</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_7_1_1_1"><i><font color="Green" title="E72">A49</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_7_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_7_1_1_2"/><i><font color="Green" title="E71">A50</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 ;<br/><div class="add"><a NAME="E2:107_4_7_1_1_2"/><b>then </b><i><font color="Green" title="E72">A51</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c10">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green" title="E69">A46</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_7_1_1_2"><i><font color="Green" title="E71">A50</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green" title="E69">A46</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_7_1_1_2"><i><font color="Green" title="E72">A51</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_7"><i><font color="Green" title="E68">A45</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_7"><i><font color="Green" title="E70">A47</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_8"><b>suppose </b></a><a NAME="E1:107_4_8"/><i><font color="Green" title="E68">A52</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c11">k1</font>, <font color="Maroon" title="c12">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_8"/><i><font color="Green" title="E69">A53</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">k1</font>,<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T44" title="SCMPDS_2:th.44">SCMPDS_2:44</a></i>;<br/><div><i><font color="Green" title="E70">A54</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_8_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_8_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_8_1_1_1"/><i><font color="Green" title="E71">A55</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_8_1_1_1"/><b>then </b><i><font color="Green" title="E72">A56</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green" title="E69">A53</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_8_1_1_1"><i><font color="Green" title="E71">A55</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green" title="E69">A53</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_8_1_1_1"><i><font color="Green" title="E72">A56</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_8_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_8_1_1_2"/><i><font color="Green" title="E71">A57</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_8_1_1_2"/><b>then </b><i><font color="Green" title="E72">A58</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green" title="E69">A53</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_8_1_1_2"><i><font color="Green" title="E71">A57</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green" title="E69">A53</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_8_1_1_2"><i><font color="Green" title="E72">A58</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_8"><i><font color="Green" title="E68">A52</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_8"><i><font color="Green" title="E70">A54</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_9"><b>suppose </b></a><a NAME="E1:107_4_9"/><i><font color="Green" title="E68">A59</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c11">k1</font>, <font color="Maroon" title="c12">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_9"/><i><font color="Green" title="E69">A60</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">k1</font>,<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></i>;<br/><div><i><font color="Green" title="E70">A61</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_9_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_9_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_9_1_1_1"/><i><font color="Green" title="E71">A62</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_9_1_1_1"/><b>then </b><i><font color="Green" title="E72">A63</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green" title="E69">A60</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_9_1_1_1"><i><font color="Green" title="E71">A62</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green" title="E69">A60</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_9_1_1_1"><i><font color="Green" title="E72">A63</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_9_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_9_1_1_2"/><i><font color="Green" title="E71">A64</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_9_1_1_2"/><b>then </b><i><font color="Green" title="E72">A65</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green" title="E69">A60</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_9_1_1_2"><i><font color="Green" title="E71">A64</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green" title="E69">A60</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_9_1_1_2"><i><font color="Green" title="E72">A65</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_9"><i><font color="Green" title="E68">A59</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_9"><i><font color="Green" title="E70">A61</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_10"><b>suppose </b></a><a NAME="E1:107_4_10"/><i><font color="Green" title="E68">A66</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c11">k1</font>, <font color="Maroon" title="c12">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_10"/><i><font color="Green" title="E69">A67</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K15" title="SCMPDS_2:func.15">MultBy</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">k1</font>,<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></i>;<br/><div><i><font color="Green" title="E70">A68</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_10_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_10_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_10_1_1_1"/><i><font color="Green" title="E71">A69</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_10_1_1_1"/><b>then </b><i><font color="Green" title="E72">A70</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green" title="E69">A67</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_10_1_1_1"><i><font color="Green" title="E71">A69</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green" title="E69">A67</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_10_1_1_1"><i><font color="Green" title="E72">A70</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_10_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_10_1_1_2"/><i><font color="Green" title="E71">A71</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_10_1_1_2"/><b>then </b><i><font color="Green" title="E72">A72</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green" title="E69">A67</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_10_1_1_2"><i><font color="Green" title="E71">A71</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green" title="E69">A67</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_10_1_1_2"><i><font color="Green" title="E72">A72</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_10"><i><font color="Green" title="E68">A66</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_10"><i><font color="Green" title="E70">A68</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11"><b>suppose </b></a><a NAME="E1:107_4_11"/><i><font color="Green" title="E68">A73</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c11">k1</font>, <font color="Maroon" title="c12">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_11"/><i><font color="Green" title="E69">A74</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">k1</font>,<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T47" title="SCMPDS_2:th.47">SCMPDS_2:47</a></i>;<br/><div><i><font color="Green" title="E70">A75</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_11_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_11_1_1_1"/><i><font color="Green" title="E71">A76</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_1"/><b>then </b><i><font color="Green" title="E72">A77</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green" title="E69">A74</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_1"><i><font color="Green" title="E71">A76</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green" title="E69">A74</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_1"><i><font color="Green" title="E72">A77</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_11_1_1_2"/><i><font color="Green" title="E71">A78</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_2"/><b>then </b><i><font color="Green" title="E72">A79</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11_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="E1:107_4_11_1_1_2_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_11_1_1_2_1_1_1"/><i><font color="Green" title="E73">A80</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E74">A81</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green" title="E69">A74</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2"><i><font color="Green" title="E71">A78</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2_1_1_1"><i><font color="Green" title="E73">A80</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green" title="E69">A74</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2"><i><font color="Green" title="E72">A79</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2_1_1_1"><i><font color="Green" title="E74">A81</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_11_1_1_2_1_1_2"/><i><font color="Green" title="E73">A82</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E74">A83</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green" title="E69">A74</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2"><i><font color="Green" title="E71">A78</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2_1_1_2"><i><font color="Green" title="E73">A82</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green" title="E69">A74</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2"><i><font color="Green" title="E72">A79</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2_1_1_2"><i><font color="Green" title="E74">A83</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">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>thus </b><a NAME="E5:107_4_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11"><i><font color="Green" title="E68">A73</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_11"><i><font color="Green" title="E70">A75</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_12"><b>suppose </b></a><a NAME="E1:107_4_12"/><i><font color="Green" title="E68">A84</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c11">k1</font>, <font color="Maroon" title="c12">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_12"/><i><font color="Green" title="E69">A85</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">k1</font> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T48" title="SCMPDS_2:th.48">SCMPDS_2:48</a></i>;<br/><div><i><font color="Green" title="E70">A86</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="107_4_12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_4_12_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_12_1_1_1"><b>suppose </b></a><a NAME="E1:107_4_12_1_1_1"/><i><font color="Green" title="E71">A87</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_12_1_1_1"/><b>then </b><i><font color="Green" title="E72">A88</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green" title="E69">A85</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_12_1_1_1"><i><font color="Green" title="E71">A87</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font></span>)</span>,<font color="Maroon" title="c12">k2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green" title="E66">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green" title="E69">A85</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_12_1_1_1"><i><font color="Green" title="E72">A88</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_12_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_12_1_1_2"/><i><font color="Green" title="E71">A89</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 ;<br/><div class="add"><a NAME="E2:107_4_12_1_1_2"/><b>then </b><i><font color="Green" title="E72">A90</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c11">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green" title="E69">A85</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_12_1_1_2"><i><font color="Green" title="E71">A89</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green" title="E69">A85</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_12_1_1_2"><i><font color="Green" title="E72">A90</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_12"><i><font color="Green" title="E68">A84</font></i></a></i>;<br/><b>thus </b><a NAME="E6:107_4_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_12"><i><font color="Green" title="E70">A86</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self" title="SCMPDS_4:th.23">Th23</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
