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

<b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>



<b>assume </b><a NAME="E1:52"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">I</font> =  <a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>;<br/>
<b>assume </b><a NAME="E2:52"/>
not  <a href="ami_7.html#K3" title="AMI_7:func.3">Out_\_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">o</font> being   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E4:52"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K3" title="AMI_7:func.3">Out_\_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:52_1"/>
( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  or <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  or <font color="Maroon" title="c5">o</font> is    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T3" title="AMI_6:th.3">AMI_6:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1"><b>suppose </b></a><a NAME="E1:52_1_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:52_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:52"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="ami_7.html#T23" target="_self" title="AMI_7:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_2"><b>suppose </b></a><a NAME="E1:52_1_2"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c6">l</font> = <font color="Maroon" title="c5">o</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E3:52_1_2"/>
<font color="Maroon" title="c6">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ;<br/><b>hence </b><a NAME="E4:52_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:52"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="ami_7.html#T22" target="_self" title="AMI_7:th.22">Th22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3"><b>suppose </b></a><a NAME="E1:52_1_3"/>
<font color="Maroon" title="c5">o</font> is    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c6">o</font> = <font color="Maroon" title="c5">o</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  ;<br/><b>consider </b><font color="Maroon" title="c7">r</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/><b>set </b><font color="Maroon" title="c8">t</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span>;<br/><a NAME="E4:52_1_3"/><i><font color="Green" title="E38">A3</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 <b>by </b><i><a class="txt" href="ami_7.html#E1:52"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="bvfunc14.html#T15" title="BVFUNC14:th.15">BVFUNC14:15</a></i>;<br/><a NAME="E5:52_1_3"/><i><font color="Green" title="E39">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 <b>by </b><i><a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>;<br/><a NAME="E6:52_1_3"/><i><font color="Green" title="E40">A5</font></i>: 
8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0
 ;<br/><a NAME="E7:52_1_3"/><i><font color="Green" title="E41">A6</font></i>: 
7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3
 ;<br/><a NAME="E8:52_1_3"/><i><font color="Green" title="E42">A7</font></i>: 
7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 ;<br/><a NAME="E9:52_1_3"/><i><font color="Green" title="E43">A8</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">w</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c6">o</font> <b>by </b><i><a class="txt" href="ami_7.html#E40"><i><font color="Green" title="E27">Lm2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c10">w1</font> = <font color="Maroon" title="c9">w</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><b>set </b><font color="Maroon" title="c11">s</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:52_1_3_1"/>
( <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> or ( <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> ) or ( <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_1_1"><b>suppose </b></a><a NAME="E1:52_1_3_1_1"/><i><font color="Green" title="E44">A9</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ;<br/><div class="add"><a NAME="E2:52_1_3_1_1"/><b>then </b><i><font color="Green" title="E45">A10</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E9:52_1_3"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>;<br/><a NAME="E3:52_1_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:52"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="ami_7.html#E1:52_1_3_1_1"><i><font color="Green" title="E44">A9</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>;<br/><b>then </b><i><font color="Green" title="E46">A11</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> = 
8 <a href="int_1.html#K5" title="INT_1:func.5">div</a> 4
<b>by </b><i><a class="txt" href="ami_7.html#E1:52"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="ami_7.html#E4:52_1_3"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="ami_7.html#E1:52_1_3_1_1"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="ami_7.html#E2:52_1_3_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a>, <a class="txt" href="ami_7.html#E5:52_1_3"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
2
<b>by </b><i><a class="txt" href="ami_7.html#E6:52_1_3"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="nat_d.html#D1" title="NAT_D:def.1">NAT_D:def 1</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> = 
7 <a href="int_1.html#K5" title="INT_1:func.5">div</a> 4
<b>by </b><i><a class="txt" href="ami_7.html#E1:52"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="ami_7.html#E4:52_1_3"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="ami_7.html#E1:52_1_3_1_1"><i><font color="Green" title="E44">A9</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a>, <a class="txt" href="ami_7.html#E5:52_1_3"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="ami_7.html#E7:52_1_3"><i><font color="Green" title="E41">A6</font></i></a>, <a class="ref" href="nat_d.html#D1" title="NAT_D:def.1">NAT_D:def 1</a></i>
;<br/><a NAME="E6:52_1_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E4:52_1_3_1_1"><i><font color="Green" title="E46">A11</font></i></a></i>;<br/><b>hence </b><a NAME="E7:52_1_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:52"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self" title="AMI_7:def.4">Def4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:52_1_3_1_2"/><i><font color="Green" title="E44">A12</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 <b>and </b><br/><a NAME="E2:52_1_3_1_2"/><i><font color="Green" title="E45">A13</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 ;<br/><div class="add"><a NAME="E3:52_1_3_1_2"/><i><font color="Green" title="E46">A14</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:52_1_3_1_2"><i><font color="Green" title="E44">A12</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>;<br/><a NAME="E4:52_1_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E9:52_1_3"><i><font color="Green" title="E43">A8</font></i></a>, <a class="txt" href="ami_7.html#E2:52_1_3_1_2"><i><font color="Green" title="E45">A13</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>;<br/><b>then </b><i><font color="Green" title="E47">A15</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> = 
7 <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 5
<b>by </b><i><a class="txt" href="ami_7.html#E4:52_1_3"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="ami_7.html#E2:52_1_3_1_2"><i><font color="Green" title="E45">A13</font></i></a>, <a class="txt" href="ami_7.html#E3:52_1_3_1_2"><i><font color="Green" title="E46">A14</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a>, <a class="txt" href="ami_7.html#E5:52_1_3"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
2
<b>by </b><i><a class="txt" href="ami_7.html#E8:52_1_3"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> = 
7 <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 4
<b>by </b><i><a class="txt" href="ami_7.html#E4:52_1_3"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="ami_7.html#E2:52_1_3_1_2"><i><font color="Green" title="E45">A13</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a>, <a class="txt" href="ami_7.html#E5:52_1_3"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
3
<b>by </b><i><a class="txt" href="ami_7.html#E7:52_1_3"><i><font color="Green" title="E41">A6</font></i></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
;<br/><a NAME="E7:52_1_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E5:52_1_3_1_2"><i><font color="Green" title="E47">A15</font></i></a></i>;<br/><b>hence </b><a NAME="E8:52_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:52"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self" title="AMI_7:def.4">Def4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_1_3"><b>suppose </b></a><a NAME="E1:52_1_3_1_3"/>
( <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> )
 ;<br/><div class="add"><a NAME="E2:52_1_3_1_3"/><b>then </b><i><font color="Green" title="E44">A16</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> )
 <b>by </b><i><a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>;<br/><a NAME="E3:52_1_3_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">w1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 0
 <b>by </b><i><a class="txt" href="ami_7.html#E9:52_1_3"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>;<br/><a NAME="E4:52_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 7</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 4</span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">o</font>
 ;<br/><b>hence </b><a NAME="E5:52_1_3_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:52"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="ami_7.html#E2:52_1_3_1_3"><i><font color="Green" title="E44">A16</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self" title="AMI_7:def.4">Def4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div>
