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<div class="add">

<b>let </b><font color="Maroon">T</font> be   <a href="ami_1.html#NM8">InsType</a> of <a href="ami_3.html#K1">SCM</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D11">AMISTD_2:def 11</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1_1"/>
( <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 8 )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">f</font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="funct_1.html#NM1">Function</a> ;<br/><b>take </b>
<font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E3:73_1_1_1_1"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">f</font>
 <b>by </b><i>, , <a class="ref" href="card_3.html#T19">CARD_3:19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_2"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_2"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_2"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_2"/><i><font color="Green">E54</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_2"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:73_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_2"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_2"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:73_1_1_1_2"/><i><font color="Green">E125</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:73_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i/>;<br/><a NAME="E17:73_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:73_1_1_1_2"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:73_1_1_1_2"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E22:73_1_1_1_2"/><i><font color="Green">E128</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:73_1_1_1_2"/><i><font color="Green">E129</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E25:73_1_1_1_2"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T47">AMI_5:47</a></i>;<br/><a NAME="E26:73_1_1_1_2"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_6.html#T15" target="_self">Th15</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E28:73_1_1_1_2"/><i><font color="Green">E132</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:73_1_1_1_2"/><i><font color="Green">E150</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">d2</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E31:73_1_1_1_2"/><i><font color="Green">E151</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">d2</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T47">AMI_5:47</a></i>;<br/><a NAME="E32:73_1_1_1_2"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T17" target="_self">Th17</a>, <a class="txt" href="ami_6.html#E9:73_1_1_1_2"><i><font color="Green">E79</font></i></a>, </i>;<br/><a NAME="E33:73_1_1_1_2"/><i><font color="Green">E153</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:73_1_1_1_2"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_2_1"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_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="E1:73_1_1_1_2_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_2_1_1_1"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_2_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_2_1_1_2"/><i><font color="Green">E156</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_6.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_2_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:73_1_1_1_2"/><b>then </b><i><font color="Green">E157</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:73_1_1_1_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">d1</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">d1</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E37:73_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_3"><b>suppose </b></a><a NAME="E1:73_1_1_1_3"/><i><font color="Green">E159</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_3"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_3"/><i><font color="Green">E160</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_3"/><i><font color="Green">E161</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_3"/><i><font color="Green">E162</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_3"/><i><font color="Green">E163</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_3"/><b>then </b><i><font color="Green">E164</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:73_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_3"/><i><font color="Green">E165</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_3"/><i><font color="Green">E166</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:73_1_1_1_3"/><i><font color="Green">E167</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:73_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i/>;<br/><a NAME="E17:73_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:73_1_1_1_3"/><i><font color="Green">E168</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:73_1_1_1_3"/><i><font color="Green">E169</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E22:73_1_1_1_3"/><i><font color="Green">E170</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:73_1_1_1_3"/><i><font color="Green">E171</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E25:73_1_1_1_3"/><i><font color="Green">E172</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T48">AMI_5:48</a></i>;<br/><a NAME="E26:73_1_1_1_3"/><i><font color="Green">E173</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_6.html#T15" target="_self">Th15</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E28:73_1_1_1_3"/><i><font color="Green">E174</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:73_1_1_1_3"/><i><font color="Green">E175</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">d2</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E31:73_1_1_1_3"/><i><font color="Green">E176</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T48">AMI_5:48</a></i>;<br/><a NAME="E32:73_1_1_1_3"/><i><font color="Green">E177</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T17" target="_self">Th17</a>, , </i>;<br/><a NAME="E33:73_1_1_1_3"/><i><font color="Green">E178</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:73_1_1_1_3"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_3_1"/><i><font color="Green">E179</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_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="E1:73_1_1_1_3_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_3_1_1_1"/><i><font color="Green">E180</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_3_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_3_1_1_2"/><i><font color="Green">E181</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_6.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_3_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:73_1_1_1_3"/><b>then </b><i><font color="Green">E182</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:73_1_1_1_3"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 2 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E37:73_1_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_4"><b>suppose </b></a><a NAME="E1:73_1_1_1_4"/><i><font color="Green">E183</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_4"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_4"/><i><font color="Green">E184</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_4"/><i><font color="Green">E185</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_4"/><i><font color="Green">E186</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_4"/><i><font color="Green">E187</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_4"/><b>then </b><i><font color="Green">E188</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:73_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_4"/><i><font color="Green">E189</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_4"/><i><font color="Green">E190</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:73_1_1_1_4"/><i><font color="Green">E191</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:73_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i/>;<br/><a NAME="E17:73_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:73_1_1_1_4"/><i><font color="Green">E192</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:73_1_1_1_4"/><i><font color="Green">E194</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E22:73_1_1_1_4"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:73_1_1_1_4"/><i><font color="Green">E196</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E25:73_1_1_1_4"/><i><font color="Green">E197</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T49">AMI_5:49</a></i>;<br/><a NAME="E26:73_1_1_1_4"/><i><font color="Green">E198</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_6.html#T15" target="_self">Th15</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E28:73_1_1_1_4"/><i><font color="Green">E199</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:73_1_1_1_4"/><i><font color="Green">E200</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">d2</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E31:73_1_1_1_4"/><i><font color="Green">E201</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T49">AMI_5:49</a></i>;<br/><a NAME="E32:73_1_1_1_4"/><i><font color="Green">E202</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T17" target="_self">Th17</a>, , </i>;<br/><a NAME="E33:73_1_1_1_4"/><i><font color="Green">E203</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:73_1_1_1_4"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_4_1"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1_1_4_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_4_1_1_1"/><i><font color="Green">E205</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_4_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_4_1_1_2"/><i><font color="Green">E206</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_6.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_4_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:73_1_1_1_4"/><b>then </b><i><font color="Green">E207</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:73_1_1_1_4"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_3.html#K5">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 3 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="ami_3.html#K5">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E37:73_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_5"><b>suppose </b></a><a NAME="E1:73_1_1_1_5"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_5"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_5"/><i><font color="Green">E209</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_5"/><i><font color="Green">E210</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_5"/><i><font color="Green">E211</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_5"/><i><font color="Green">E212</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_5"/><b>then </b><i><font color="Green">E213</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:73_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_5"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_5"/><i><font color="Green">E215</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:73_1_1_1_5"/><i><font color="Green">E216</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:73_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i/>;<br/><a NAME="E17:73_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:73_1_1_1_5"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:73_1_1_1_5"/><i><font color="Green">E218</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E22:73_1_1_1_5"/><i><font color="Green">E219</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:73_1_1_1_5"/><i><font color="Green">E220</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E25:73_1_1_1_5"/><i><font color="Green">E221</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T50">AMI_5:50</a></i>;<br/><a NAME="E26:73_1_1_1_5"/><i><font color="Green">E222</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_6.html#T15" target="_self">Th15</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E28:73_1_1_1_5"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:73_1_1_1_5"/><i><font color="Green">E224</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">d2</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E31:73_1_1_1_5"/><i><font color="Green">E225</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T50">AMI_5:50</a></i>;<br/><a NAME="E32:73_1_1_1_5"/><i><font color="Green">E226</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T17" target="_self">Th17</a>, , </i>;<br/><a NAME="E33:73_1_1_1_5"/><i><font color="Green">E227</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:73_1_1_1_5"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_5_1"/><i><font color="Green">E228</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1_1_5_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_5_1_1_1"/><i><font color="Green">E229</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_5_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_5_1_1_2"/><i><font color="Green">E230</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_6.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_5_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:73_1_1_1_5"/><b>then </b><i><font color="Green">E231</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:73_1_1_1_5"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 4 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E37:73_1_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_6"><b>suppose </b></a><a NAME="E1:73_1_1_1_6"/><i><font color="Green">E232</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_6"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_6"/><i><font color="Green">E233</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_6"/><i><font color="Green">E234</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_6"/><i><font color="Green">E235</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_6"/><i><font color="Green">E236</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_6"/><b>then </b><i><font color="Green">E237</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:73_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_6"/><i><font color="Green">E238</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_6"/><i><font color="Green">E239</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:73_1_1_1_6"/><i><font color="Green">E240</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:73_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i/>;<br/><a NAME="E17:73_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:73_1_1_1_6"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:73_1_1_1_6"/><i><font color="Green">E242</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E22:73_1_1_1_6"/><i><font color="Green">E243</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:73_1_1_1_6"/><i><font color="Green">E244</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E25:73_1_1_1_6"/><i><font color="Green">E245</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T51">AMI_5:51</a></i>;<br/><a NAME="E26:73_1_1_1_6"/><i><font color="Green">E246</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_6.html#T15" target="_self">Th15</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E28:73_1_1_1_6"/><i><font color="Green">E247</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:73_1_1_1_6"/><i><font color="Green">E248</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">d2</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E31:73_1_1_1_6"/><i><font color="Green">E249</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T51">AMI_5:51</a></i>;<br/><a NAME="E32:73_1_1_1_6"/><i><font color="Green">E250</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T17" target="_self">Th17</a>, , </i>;<br/><a NAME="E33:73_1_1_1_6"/><i><font color="Green">E251</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:73_1_1_1_6"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_6_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_6_1"/><i><font color="Green">E252</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1_1_6_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_6_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_6_1_1_1"/><i><font color="Green">E253</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_6_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_6_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_6_1_1_2"/><i><font color="Green">E254</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_6.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_6_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:73_1_1_1_6"/><b>then </b><i><font color="Green">E255</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:73_1_1_1_6"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 5 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E37:73_1_1_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_7"><b>suppose </b></a><a NAME="E1:73_1_1_1_7"/><i><font color="Green">E256</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_7"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_7"/><i><font color="Green">E257</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_7"/><i><font color="Green">E258</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_7"/><i><font color="Green">E259</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_7"/><i><font color="Green">E260</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_7"/><b>then </b><i><font color="Green">E261</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E10:73_1_1_1_7"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_7"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_7"/><i><font color="Green">E262</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_7"/><i><font color="Green">E263</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E16:73_1_1_1_7"/><i><font color="Green">E264</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E17:73_1_1_1_7"/><i><font color="Green">E265</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E19:73_1_1_1_7"/><i><font color="Green">E266</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <font color="Maroon">i1</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T11" target="_self">Th11</a>, <a class="ref" href="ami_5.html#T52">AMI_5:52</a></i>;<br/><a NAME="E20:73_1_1_1_7"/><i><font color="Green">E267</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E21:73_1_1_1_7"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_7_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E2:73_1_1_1_7_1"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:73_1_1_1_7_1"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, </i>;<br/>


</div><b>end;</b></div><a NAME="E22:73_1_1_1_7"/><b>then </b><i><font color="Green">E268</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E23:73_1_1_1_7"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 6 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E24:73_1_1_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_8"><b>suppose </b></a><a NAME="E1:73_1_1_1_8"/><i><font color="Green">E269</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_8"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_8"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_8"/><i><font color="Green">E270</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_8"/><i><font color="Green">E271</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_8"/><i><font color="Green">E272</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_8"/><i><font color="Green">E273</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_8"/><b>then </b><i><font color="Green">E274</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:73_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_8"/><i><font color="Green">E275</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_8"/><i><font color="Green">E276</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:73_1_1_1_8"/><i><font color="Green">E277</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:73_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i/>;<br/><a NAME="E17:73_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:73_1_1_1_8"/><i><font color="Green">E278</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:73_1_1_1_8"/><i><font color="Green">E279</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E22:73_1_1_1_8"/><i><font color="Green">E280</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:73_1_1_1_8"/><i><font color="Green">E281</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">d1</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E25:73_1_1_1_8"/><i><font color="Green">E282</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T53">AMI_5:53</a></i>;<br/><a NAME="E26:73_1_1_1_8"/><i><font color="Green">E283</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d1</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_6.html#T15" target="_self">Th15</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E28:73_1_1_1_8"/><i><font color="Green">E284</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:73_1_1_1_8"/><i><font color="Green">E285</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">d2</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E31:73_1_1_1_8"/><i><font color="Green">E286</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i2</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T53">AMI_5:53</a></i>;<br/><a NAME="E32:73_1_1_1_8"/><i><font color="Green">E287</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i2</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T17" target="_self">Th17</a>, , </i>;<br/><a NAME="E33:73_1_1_1_8"/><i><font color="Green">E288</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:73_1_1_1_8"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_8_1"/><i><font color="Green">E289</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_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="E1:73_1_1_1_8_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_8_1_1_1"/><i><font color="Green">E290</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_8_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_8_1_1_2"/><i><font color="Green">E291</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_6.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_8_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:73_1_1_1_8"/><b>then </b><i><font color="Green">E292</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:73_1_1_1_8"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 7 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E37:73_1_1_1_8"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_9"><b>suppose </b></a><a NAME="E1:73_1_1_1_9"/><i><font color="Green">E293</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:73_1_1_1_9"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:73_1_1_1_9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:73_1_1_1_9"/><i><font color="Green">E294</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:73_1_1_1_9"/><i><font color="Green">E295</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:73_1_1_1_9"/><i><font color="Green">E296</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:73_1_1_1_9"/><i><font color="Green">E297</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E9:73_1_1_1_9"/><b>then </b><i><font color="Green">E298</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:73_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><a NAME="E11:73_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="ami_6.html#T7" target="_self">Th7</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:73_1_1_1_9"/><i><font color="Green">E299</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:73_1_1_1_9"/><i><font color="Green">E300</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:73_1_1_1_9"/><i><font color="Green">E301</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:73_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i/>;<br/><a NAME="E17:73_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="ref" href="ami_6.html#T10" target="_self">Th10</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:73_1_1_1_9"/><i><font color="Green">E302</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:73_1_1_1_9"/><i><font color="Green">E303</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E22:73_1_1_1_9"/><i><font color="Green">E304</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:73_1_1_1_9"/><i><font color="Green">E305</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T8" target="_self">Th8</a></i>;<br/><b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">d1</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E25:73_1_1_1_9"/><i><font color="Green">E306</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Maroon">i1</font>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T54">AMI_5:54</a></i>;<br/><a NAME="E26:73_1_1_1_9"/><i><font color="Green">E307</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d1</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_6.html#T15" target="_self">Th15</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E28:73_1_1_1_9"/><i><font color="Green">E308</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:73_1_1_1_9"/><i><font color="Green">E309</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">d2</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E31:73_1_1_1_9"/><i><font color="Green">E310</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Maroon">i2</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T54">AMI_5:54</a></i>;<br/><a NAME="E32:73_1_1_1_9"/><i><font color="Green">E311</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i2</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T17" target="_self">Th17</a>, , </i>;<br/><a NAME="E33:73_1_1_1_9"/><i><font color="Green">E312</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:73_1_1_1_9"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1_9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:73_1_1_1_9_1"/><i><font color="Green">E313</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_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="E1:73_1_1_1_9_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1_9_1_1_1"/><i><font color="Green">E314</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="ami_6.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_6.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_9_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_1_9_1_1_2"/><i><font color="Green">E315</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="ami_6.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_6.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:73_1_1_1_9_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:73_1_1_1_9"/><b>then </b><i><font color="Green">E316</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="ami_6.html#E8"><i><font color="Green">Lemma64</font></i></a>, <a class="txt" href="ami_6.html#E9"><i><font color="Green">Lemma66</font></i></a>, <a class="ref" href="ami_6.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:73_1_1_1_9"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 8 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E37:73_1_1_1_9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
