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

<b>let </b><font color="Maroon" title="c6">W</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:103"/><i><font color="Green" title="E57">A1</font></i>: 
<font color="Maroon" title="c6">W</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 ;<br/>

<b>set </b><font color="Maroon" title="c7">I</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0;<br/>
<b>assume </b><a NAME="E2:103"/><i><font color="Green" title="E58">A2</font></i>: 
 <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">W</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:103_1"/>
(  ex <font color="Olive" title="b1">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">k1</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Olive" title="b2">k1</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Olive" title="b3">k2</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Olive" title="b3">k2</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Olive" title="b3">k2</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <font color="Olive" title="b3">k2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b4">k2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font> )
 </span><b>by </b><i><a class="ref" href="scmpds_2.html#T91" target="_self" title="SCMPDS_2:th.91">Th91</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1"><b>suppose </b></a><a NAME="E1:103_1_1"/>
 ex <font color="Olive" title="b1">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">k1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c8">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:103_1_1"/><i><font color="Green" title="E59">A3</font></i>: 
<font color="Maroon" title="c6">W</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="c8">k1</font>
 ;<br/><b>thus </b><a NAME="E4:103_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="scmpds_2.html#E2:103"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="scmpds_2.html#E3:103_1_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="scmpds_2.html#T85" target="_self" title="SCMPDS_2:th.85">Th85</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_2"><b>suppose </b></a><a NAME="E1:103_1_2"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T89" target="_self" title="SCMPDS_2:th.89">Th89</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_3"><b>suppose </b></a><a NAME="E1:103_1_3"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T90" target="_self" title="SCMPDS_2:th.90">Th90</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_4"><b>suppose </b></a><a NAME="E1:103_1_4"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Olive" title="b2">k1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T77" target="_self" title="SCMPDS_2:th.77">Th77</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_5"><b>suppose </b></a><a NAME="E1:103_1_5"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Olive" title="b3">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_5"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T78" target="_self" title="SCMPDS_2:th.78">Th78</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_6"><b>suppose </b></a><a NAME="E1:103_1_6"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Olive" title="b3">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_6"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T86" target="_self" title="SCMPDS_2:th.86">Th86</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_7"><b>suppose </b></a><a NAME="E1:103_1_7"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Olive" title="b3">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_7"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T87" target="_self" title="SCMPDS_2:th.87">Th87</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_8"><b>suppose </b></a><a NAME="E1:103_1_8"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <font color="Olive" title="b3">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_8"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T88" target="_self" title="SCMPDS_2:th.88">Th88</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_9"><b>suppose </b></a><a NAME="E1:103_1_9"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b4">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_9"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T80" target="_self" title="SCMPDS_2:th.80">Th80</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_10"><b>suppose </b></a><a NAME="E1:103_1_10"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_10"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T81" target="_self" title="SCMPDS_2:th.81">Th81</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_11"><b>suppose </b></a><a NAME="E1:103_1_11"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_11"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T82" target="_self" title="SCMPDS_2:th.82">Th82</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_12"><b>suppose </b></a><a NAME="E1:103_1_12"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_12"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T83" target="_self" title="SCMPDS_2:th.83">Th83</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_13"><b>suppose </b></a><a NAME="E1:103_1_13"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</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="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_13"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T84" target="_self" title="SCMPDS_2:th.84">Th84</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_14"><b>suppose </b></a><a NAME="E1:103_1_14"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">k1</font> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">k2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:103_1_14"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:103"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="scmpds_2.html#T79" target="_self" title="SCMPDS_2:th.79">Th79</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
