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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:107"/><i><font color="Green">E57</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E2:107"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmpds_4.html#R1" target="_self">valid_at</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:107"/><i><font color="Green">E59</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:107"/><i><font color="Green">E60</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 3
 <b>and </b><br/><a NAME="E5:107"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E6:107"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="ami_2.html#K2">SCM-Data-Loc</a> ;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E8:107"/><i><font color="Green">E63</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T32">SCMPDS_3:32</a></i>;<br/>
<a NAME="E9:107"/><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_2.html#K18">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>2</sub></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">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E8:107"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_4.html#T70" target="_self">Th70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T70" target="_self">Th70</a></i>
<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scmpds_4.html#E8:107"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<div><i><font color="Green">E65</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">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 5 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 6 )
 ;<br/><a NAME="E2:107_2"/><b>then </b><i><font color="Green">E66</font></i>: 
not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,1,4,5,6</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E2:107_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmpds_4.html#T6" target="_self">Th6</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmpds_4.html#T6" target="_self">Th6</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/><br/></div><b>end;</b></div>
<div><i><font color="Green">E66</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">c<sub>9</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E12:107"/><i><font color="Green">E67</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 13
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T15">SCMPDS_2:15</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="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">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 13 )
 </span><b>by </b><i><a class="txt" href="scmpds_4.html#E3:107"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmpds_4.html#E4:107"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scmpds_4.html#E12:107"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmpds_3.html#T1">SCMPDS_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_1"><b>suppose </b></a><a NAME="E1:107_4_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_1"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K4">goto</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><div><i><font color="Green">E69</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">c<sub>10</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
;<br/></div><b>end;</b></div> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self">Th82</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/><br/><b>thus </b><a NAME="E7:107_4_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>10</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T37">SCMPDS_2:37</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>11</sub></font> be    <a href="scmpds_2.html#M1">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">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></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">E71</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_2_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_2_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_2_1_1_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_2_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_2"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_3"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="scmpds_2.html#K8">&lt;&gt;0_goto</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><div><i><font color="Green">E69</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">c<sub>12</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T67">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">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</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">E70</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_3_2_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_3_2_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self">Th82</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_3_2_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<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">E70</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_3_2_1_2"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_3_2_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_3"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_3_2_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/><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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_4"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><div><i><font color="Green">E69</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">c<sub>12</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T68">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">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&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">E70</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_4_2_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_4_2_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self">Th82</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_4_2_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<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">E70</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_4_2_1_2"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_4_2_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_4"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_4_2_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/><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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_4"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_5"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:107"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><div><i><font color="Green">E69</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">c<sub>12</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T69">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">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&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">E70</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_5_2_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_5_2_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:107"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmpds_4.html#E5:107"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_4.html#T82" target="_self">Th82</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_5_2_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<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">E70</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:107_4_5_2_1_2"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_5_2_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E9:107"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmpds_4.html#E3:107_4_5"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_5_2_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T69">SCMPDS_2:69</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/><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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_5"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_6"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="scmpds_2.html#K11">:=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T42">SCMPDS_2:42</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>12</sub></font> be    <a href="scmpds_2.html#M1">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></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">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_6_1_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_6_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_6_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_6_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_6_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_6_1_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_6_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_6"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_6_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_6"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_6"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_7"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K12">AddTo</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T43">SCMPDS_2:43</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>12</sub></font> be    <a href="scmpds_2.html#M1">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></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">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_7_1_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_7_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_7_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_7_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_7_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_7_1_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_7_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_7_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_7"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_7"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_8"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K13">AddTo</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T44">SCMPDS_2:44</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>13</sub></font> be    <a href="scmpds_2.html#M1">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></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">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_8_1_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_8_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_8_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_8_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_8_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_8_1_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_8_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_8"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_8_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_8"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_8"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_9"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K14">SubFrom</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T45">SCMPDS_2:45</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>13</sub></font> be    <a href="scmpds_2.html#M1">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></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">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_9_1_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_9_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_9_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_9_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_9_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_9_1_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_9_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_9"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_9_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_9"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_9"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_10"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K15">MultBy</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T46">SCMPDS_2:46</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>13</sub></font> be    <a href="scmpds_2.html#M1">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></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">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_10_1_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_10_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_10_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_10_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_10_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_10_1_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_10_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_10"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_10_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_10"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_10"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_11"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K16">Divide</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T47">SCMPDS_2:47</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>13</sub></font> be    <a href="scmpds_2.html#M1">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></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">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_11_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_11_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></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">E73</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E74</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2_1_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2_1_1_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="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">E73</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_11_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E74</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11_1_1_2_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_11"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_11_1_1_2_1_1_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_11"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_11"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">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">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 13
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:107_4_12"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="scmpds_2.html#K17">:=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T48">SCMPDS_2:48</a></i>;<br/><div><i><font color="Green">E70</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">c<sub>13</sub></font> be    <a href="scmpds_2.html#M1">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">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> or  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></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">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_12_1_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_12_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_4.html#E11:107"><i><font color="Green">E66</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_12_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_4_12_1_1_2"><b>suppose </b></a><a NAME="E1:107_4_12_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_4_12_1_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_12_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E6:107"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:107_4_12"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmpds_4.html#E2:107_4_12_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>thus </b><a NAME="E5:107_4_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E10:107"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmpds_4.html#E1:107_4_12"><i><font color="Green">E68</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">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_4.html#E4:107_4_12"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T23" target="_self">Th23</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
