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

<b>let </b><font color="Maroon">a</font> be    <a href="ami_3.html#M1">Data-Location</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="ami_3.html#M1">Data-Location</a> ;<br/>



<b>set </b><font color="Maroon">I</font> =  <a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>
<b>assume </b><a NAME="E1:50"/>
not  <a href="ami_7.html#K3" target="_self">Out_\_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">o</font> being   <a href="ami_1.html#NM1">Object</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:50"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="ami_7.html#K3" target="_self">Out_\_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:50_1"/>
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  or <font color="Maroon">o</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  or <font color="Maroon">o</font> is    <a href="ami_3.html#M1">Data-Location</a>  )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T3">AMI_6:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_1"><b>suppose </b></a><a NAME="E1:50_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:50_1_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_2"><b>suppose </b></a><a NAME="E1:50_1_2"/>
<font color="Maroon">o</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:50_1_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_3"><b>suppose </b></a><a NAME="E1:50_1_3"/>
<font color="Maroon">o</font> is    <a href="ami_3.html#M1">Data-Location</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">o</font> = <font color="Maroon">o</font> as    <a href="ami_3.html#M1">Data-Location</a>  ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:50_1_3_1"/>
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_3_1_1"><b>suppose </b></a><a NAME="E1:50_1_3_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:50_1_3_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>;<br/><b>reconsider </b><font color="Maroon">w</font> = <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">o</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">w1</font> = <font color="Maroon">w</font> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>set </b><font color="Maroon">s</font> = <font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font>;<br/><i><font color="Green">E52</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<font color="Maroon">w1</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_7.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_3_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:50_1_3_1_1_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_3_1_1_2_1"><b>suppose </b></a><a NAME="E1:50_1_3_1_1_2_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:50_1_3_1_1_2_1"/><b>then </b><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="square_1.html#K3">^2</a> 
 <b>by </b><i/>;<br/><a NAME="E3:50_1_3_1_1_2_1"/><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w1</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">w1</font>
 <b>by </b><i>, <a class="ref" href="ami_7.html#T4" target="_self">Th4</a>, , <a class="ref" href="ami_7.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_3_1_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_1_3_1_1_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font>
 ;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 0 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="square_1.html#K3">^2</a> 
<b>by </b><i><a class="txt" href="ami_7.html#E3:50"><i><font color="Green">E44</font></i></a>, <a class="ref" href="ami_7.html#T5" target="_self">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>

;<br/><a NAME="E3:50_1_3_1_1_2_1_1"/><b>then </b>
0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/><a NAME="E4:50_1_3_1_1_2_1_1"/><b>then </b>
2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> 0 <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><a NAME="E5:50_1_3_1_1_2_1_1"/><b>then </b><i><font color="Green">E95</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 ;<br/><a NAME="E6:50_1_3_1_1_2_1_1"/><i><font color="Green">E96</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 1 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E7:50_1_3_1_1_2_1_1"/>
(  <a href="xcmplx_0.html#K4">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="xcmplx_0.html#K4">-</a> 1 )
 ;<br/><a NAME="E8:50_1_3_1_1_2_1_1"/><b>then </b>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> 1
 <b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/><b>hence </b><a NAME="E9:50_1_3_1_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E1:50_1_3_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="int_1.html#T47">INT_1:47</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:50_1_3_1_1_2_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_3_1_1_2_2"><b>suppose </b></a><a NAME="E1:50_1_3_1_1_2_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">r</font> = <font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1;<br/><b>reconsider </b><font color="Maroon">w</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">o</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">w1</font> = <font color="Maroon">w</font> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>set </b><font color="Maroon">s</font> = <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font>;<br/><a NAME="E4:50_1_3_1_1_2_2"/><i><font color="Green">E104</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><i><font color="Green">E105</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<font color="Maroon">w1</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="txt" href="ami_7.html#E3:50"><i><font color="Green">E44</font></i></a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><a NAME="E6:50_1_3_1_1_2_2"/><i><font color="Green">E106</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_3_1_1_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_1_3_1_1_2_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font>
 ;<br/><a NAME="E2:50_1_3_1_1_2_2_2"/><b>then </b><i><font color="Green">E107</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="ami_7.html#T5" target="_self">Th5</a>, <a class="ref" href="ami_7.html#T6" target="_self">Th6</a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>;<br/><a NAME="E3:50_1_3_1_1_2_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="ami_7.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>;<br/><a NAME="E4:50_1_3_1_1_2_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">b</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="txt" href="ami_7.html#E1:50_1_3_1_1"><i><font color="Green">E47</font></i></a></i>;<br/><b>hence </b><a NAME="E5:50_1_3_1_1_2_2_2"/>
contradiction
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:50_1_3_1_1_2_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_3_1_2"><b>suppose </b></a><a NAME="E1:50_1_3_1_2"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:50_1_3_1_2"/><b>then </b><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
 <b>by </b><i><a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>;<br/><b>reconsider </b><font color="Maroon">w</font> = <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">o</font> <b>by </b><i/>;<br/><b>set </b><font color="Maroon">s</font> = <font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> = 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<font color="Maroon">w</font>
<b>by </b><i><a class="ref" href="ami_7.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><a NAME="E5:50_1_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">o</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:50_1_3_1_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div>
