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<b>let </b><font color="Maroon" title="c1">i</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Olive" title="b2">s2</font> &amp;  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 holds <br/> <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Olive" title="b1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Olive" title="b2">s2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c3">s2</font> &amp;  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 implies  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:66"/><i><font color="Green" title="E41">A1</font></i>: 
(  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c3">s2</font> &amp;  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 )
 </span><b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="nat_1.html#T38" title="NAT_1:th.38">NAT_1:38</a>, <a class="ref" href="scmpds_2.html#T15" title="SCMPDS_2:th.15">SCMPDS_2:15</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1"><b>suppose </b></a><a NAME="E1:66_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_1"/><i><font color="Green" title="E42">A2</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <font color="Maroon" title="c4">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T35" title="SCMPDS_2:th.35">SCMPDS_2:35</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_1"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_2"><b>suppose </b></a><a NAME="E1:66_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <b> such that </b><br/><a NAME="E3:66_1_2"/><i><font color="Green" title="E42">A3</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T36" title="SCMPDS_2:th.36">SCMPDS_2:36</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_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="E1:66_1_2_1_1"/>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> or <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_2_1_1_1"/><i><font color="Green" title="E43">A4</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E3:66_1_2"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_2"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="#E1:66_1_2_1_1_1"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_2_1_1_2"/><i><font color="Green" title="E43">A5</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_2"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_2"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="#E1:66_1_2_1_1_2"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_2"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_3"><b>suppose </b></a><a NAME="E1:66_1_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c5">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_3"/><i><font color="Green" title="E42">A6</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c5">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T37" title="SCMPDS_2:th.37">SCMPDS_2:37</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_3_1_1"/>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b</font> or <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_3_1_1_1"/><i><font color="Green" title="E43">A7</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c6">b</font> = 
<font color="Maroon" title="c5">k1</font>
<b>by </b><i><a class="txt" href="#E3:66_1_3"><i><font color="Green" title="E42">A6</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c6">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_3"><i><font color="Green" title="E42">A6</font></i></a>, <a class="txt" href="#E1:66_1_3_1_1_1"><i><font color="Green" title="E43">A7</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_3_1_1_2"/><i><font color="Green" title="E43">A8</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c6">b</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c6">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_3"><i><font color="Green" title="E42">A6</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c6">b</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c6">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_3"><i><font color="Green" title="E42">A6</font></i></a>, <a class="txt" href="#E1:66_1_3_1_1_2"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_3"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_4"><b>suppose </b></a><a NAME="E1:66_1_4"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c5">k1</font>, <font color="Maroon" title="c6">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_4"/><i><font color="Green" title="E42">A9</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Maroon" title="c6">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T39" title="SCMPDS_2:th.39">SCMPDS_2:39</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_4"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_4"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_4"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_5"><b>suppose </b></a><a NAME="E1:66_1_5"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c5">k1</font>, <font color="Maroon" title="c6">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_5"/><i><font color="Green" title="E42">A10</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c6">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T40" title="SCMPDS_2:th.40">SCMPDS_2:40</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_5"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_5"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_5"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_6"><b>suppose </b></a><a NAME="E1:66_1_6"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c5">k1</font>, <font color="Maroon" title="c6">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_6"/><i><font color="Green" title="E42">A11</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <font color="Maroon" title="c6">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T41" title="SCMPDS_2:th.41">SCMPDS_2:41</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_6"><i><font color="Green" title="E42">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="#E3:66_1_6"><i><font color="Green" title="E42">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_6"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_7"><b>suppose </b></a><a NAME="E1:66_1_7"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c5">k1</font>, <font color="Maroon" title="c6">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_7"/><i><font color="Green" title="E42">A12</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">k1</font> <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Maroon" title="c6">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T42" title="SCMPDS_2:th.42">SCMPDS_2:42</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_7_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_7_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_7_1_1_1"/><i><font color="Green" title="E43">A13</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_7_1_1_1"/><b>then </b><i><font color="Green" title="E44">A14</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font> = 
<font color="Maroon" title="c6">k2</font>
<b>by </b><i><a class="txt" href="#E3:66_1_7"><i><font color="Green" title="E42">A12</font></i></a>, <a class="txt" href="#E1:66_1_7_1_1_1"><i><font color="Green" title="E43">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_7"><i><font color="Green" title="E42">A12</font></i></a>, <a class="txt" href="#E2:66_1_7_1_1_1"><i><font color="Green" title="E44">A14</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_7_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_7_1_1_2"/><i><font color="Green" title="E43">A15</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_7_1_1_2"/><b>then </b><i><font color="Green" title="E44">A16</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_7"><i><font color="Green" title="E42">A12</font></i></a>, <a class="txt" href="#E1:66_1_7_1_1_2"><i><font color="Green" title="E43">A15</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_7"><i><font color="Green" title="E42">A12</font></i></a>, <a class="txt" href="#E2:66_1_7_1_1_2"><i><font color="Green" title="E44">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_7"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_8"><b>suppose </b></a><a NAME="E1:66_1_8"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c5">k1</font>, <font color="Maroon" title="c6">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_8"/><i><font color="Green" title="E42">A17</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">k1</font>,<font color="Maroon" title="c6">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T43" title="SCMPDS_2:th.43">SCMPDS_2:43</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_8_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_8_1_1_1"/><i><font color="Green" title="E43">A18</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_8_1_1_1"/><b>then </b><i><font color="Green" title="E44">A19</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k2</font>
<b>by </b><i><a class="txt" href="#E3:66_1_8"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="#E1:66_1_8_1_1_1"><i><font color="Green" title="E43">A18</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k2</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_8"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="#E2:66_1_8_1_1_1"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_8_1_1_2"/><i><font color="Green" title="E43">A20</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_8_1_1_2"/><b>then </b><i><font color="Green" title="E44">A21</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_8"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="#E1:66_1_8_1_1_2"><i><font color="Green" title="E43">A20</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E3:66_1_8"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="#E2:66_1_8_1_1_2"><i><font color="Green" title="E44">A21</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_8"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_9"><b>suppose </b></a><a NAME="E1:66_1_9"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c6">k1</font>, <font color="Maroon" title="c7">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_9"/><i><font color="Green" title="E42">A22</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T44" title="SCMPDS_2:th.44">SCMPDS_2:44</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_9_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_9_1_1_1"/><i><font color="Green" title="E43">A23</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_9_1_1_1"/><b>then </b><i><font color="Green" title="E44">A24</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:66_1_9"><i><font color="Green" title="E42">A22</font></i></a>, <a class="txt" href="#E1:66_1_9_1_1_1"><i><font color="Green" title="E43">A23</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_9"><i><font color="Green" title="E42">A22</font></i></a>, <a class="txt" href="#E2:66_1_9_1_1_1"><i><font color="Green" title="E44">A24</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_9_1_1_2"/><i><font color="Green" title="E43">A25</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_9_1_1_2"/><b>then </b><i><font color="Green" title="E44">A26</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_9"><i><font color="Green" title="E42">A22</font></i></a>, <a class="txt" href="#E1:66_1_9_1_1_2"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_9"><i><font color="Green" title="E42">A22</font></i></a>, <a class="txt" href="#E2:66_1_9_1_1_2"><i><font color="Green" title="E44">A26</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_9"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_10"><b>suppose </b></a><a NAME="E1:66_1_10"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c6">k1</font>, <font color="Maroon" title="c7">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_10"/><i><font color="Green" title="E42">A27</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_10_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_10_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_10_1_1_1"/><i><font color="Green" title="E43">A28</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_10_1_1_1"/><b>then </b><i><font color="Green" title="E44">A29</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:66_1_10"><i><font color="Green" title="E42">A27</font></i></a>, <a class="txt" href="#E1:66_1_10_1_1_1"><i><font color="Green" title="E43">A28</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_10"><i><font color="Green" title="E42">A27</font></i></a>, <a class="txt" href="#E2:66_1_10_1_1_1"><i><font color="Green" title="E44">A29</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_10_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_10_1_1_2"/><i><font color="Green" title="E43">A30</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_10_1_1_2"/><b>then </b><i><font color="Green" title="E44">A31</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_10"><i><font color="Green" title="E42">A27</font></i></a>, <a class="txt" href="#E1:66_1_10_1_1_2"><i><font color="Green" title="E43">A30</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_10"><i><font color="Green" title="E42">A27</font></i></a>, <a class="txt" href="#E2:66_1_10_1_1_2"><i><font color="Green" title="E44">A31</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_10"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_11"><b>suppose </b></a><a NAME="E1:66_1_11"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c6">k1</font>, <font color="Maroon" title="c7">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_11"/><i><font color="Green" title="E42">A32</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K15" title="SCMPDS_2:func.15">MultBy</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_11_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_11_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_11_1_1_1"/><i><font color="Green" title="E43">A33</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_11_1_1_1"/><b>then </b><i><font color="Green" title="E44">A34</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:66_1_11"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="#E1:66_1_11_1_1_1"><i><font color="Green" title="E43">A33</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_11"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="#E2:66_1_11_1_1_1"><i><font color="Green" title="E44">A34</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_11_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_11_1_1_2"/><i><font color="Green" title="E43">A35</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_11_1_1_2"/><b>then </b><i><font color="Green" title="E44">A36</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_11"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="#E1:66_1_11_1_1_2"><i><font color="Green" title="E43">A35</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_11"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="#E2:66_1_11_1_1_2"><i><font color="Green" title="E44">A36</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_11"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_12"><b>suppose </b></a><a NAME="E1:66_1_12"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c6">k1</font>, <font color="Maroon" title="c7">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_12"/><i><font color="Green" title="E42">A37</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T47" title="SCMPDS_2:th.47">SCMPDS_2:47</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_12_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_12_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_12_1_1_1"/><i><font color="Green" title="E43">A38</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_12_1_1_1"/><b>then </b><i><font color="Green" title="E44">A39</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:66_1_12"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="#E1:66_1_12_1_1_1"><i><font color="Green" title="E43">A38</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_12"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="#E2:66_1_12_1_1_1"><i><font color="Green" title="E44">A39</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_12_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_12_1_1_2"/><i><font color="Green" title="E43">A40</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_12_1_1_2"/><b>then </b><i><font color="Green" title="E44">A41</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_12_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_12_1_1_2_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_12_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_12_1_1_2_1_1_1"/><i><font color="Green" title="E45">A42</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font></span><br/><div class="add"><a NAME="E2:66_1_12_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E46">A43</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_12"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="#E1:66_1_12_1_1_2"><i><font color="Green" title="E43">A40</font></i></a>, <a class="txt" href="#E1:66_1_12_1_1_2_1_1_1"><i><font color="Green" title="E45">A42</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_12"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="#E2:66_1_12_1_1_2"><i><font color="Green" title="E44">A41</font></i></a>, <a class="txt" href="#E2:66_1_12_1_1_2_1_1_1"><i><font color="Green" title="E46">A43</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_12_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_12_1_1_2_1_1_2"/><i><font color="Green" title="E45">A44</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font></span><br/><div class="add"><a NAME="E2:66_1_12_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E46">A45</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:66_1_12"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="#E1:66_1_12_1_1_2"><i><font color="Green" title="E43">A40</font></i></a>, <a class="txt" href="#E1:66_1_12_1_1_2_1_1_2"><i><font color="Green" title="E45">A44</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_12"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="#E2:66_1_12_1_1_2"><i><font color="Green" title="E44">A41</font></i></a>, <a class="txt" href="#E2:66_1_12_1_1_2_1_1_2"><i><font color="Green" title="E46">A45</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_12"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_13"><b>suppose </b></a><a NAME="E1:66_1_13"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c6">k1</font>, <font color="Maroon" title="c7">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:66_1_13"/><i><font color="Green" title="E42">A46</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">k1</font> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T48" title="SCMPDS_2:th.48">SCMPDS_2:48</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_13_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_13_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_13_1_1_1"/><i><font color="Green" title="E43">A47</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_13_1_1_1"/><b>then </b><i><font color="Green" title="E44">A48</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:66_1_13"><i><font color="Green" title="E42">A46</font></i></a>, <a class="txt" href="#E1:66_1_13_1_1_1"><i><font color="Green" title="E43">A47</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">b</font></span>)</span>,<font color="Maroon" title="c7">k2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_3.html#T3" title="SCMPDS_3:th.3">SCMPDS_3:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_13"><i><font color="Green" title="E42">A46</font></i></a>, <a class="txt" href="#E2:66_1_13_1_1_1"><i><font color="Green" title="E44">A48</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_13_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_13_1_1_2"/><i><font color="Green" title="E43">A49</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:66_1_13_1_1_2"/><b>then </b><i><font color="Green" title="E44">A50</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c2">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_13"><i><font color="Green" title="E42">A46</font></i></a>, <a class="txt" href="#E1:66_1_13_1_1_2"><i><font color="Green" title="E43">A49</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon" title="c3">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:66_1_13"><i><font color="Green" title="E42">A46</font></i></a>, <a class="txt" href="#E2:66_1_13_1_1_2"><i><font color="Green" title="E44">A50</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:66_1_13"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
