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<b>let </b><font color="Maroon" title="c2">T</font> be   <a href="ami_1.html#NM10" title="AMI_1:NM.10">InsType</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D11" title="AMISTD_2:def.11">AMISTD_2:def 11</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:99_1_1_1"/>
( <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E26"><i><font color="Green" title="E24">Lm3</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_1"><b>suppose </b></a><a NAME="E1:99_1_1_1_1"/><i><font color="Green" title="E65">A1</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon" title="c3">f</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/><b>take </b>
<font color="Maroon" title="c3">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E3:99_1_1_1_1"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_1"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="scmring3.html#T32" target="_self" title="SCMRING3:th.32">Th32</a>, <a class="ref" href="card_3.html#T19" title="CARD_3:th.19">CARD_3:19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_2"><b>suppose </b></a><a NAME="E1:99_1_1_1_2"/><i><font color="Green" title="E65">A2</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>take </b>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E2:99_1_1_1_2"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T94" title="CARD_3:th.94">CARD_3:94</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:99_1_1_1_2"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:99_1_1_1_2"/><i><font color="Green" title="E66">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:99_1_1_1_2"/><i><font color="Green" title="E67">A4</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:99_1_1_1_2"/><i><font color="Green" title="E68">A5</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/><a NAME="E8:99_1_1_1_2"/><i><font color="Green" title="E69">A6</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_2"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="scmring3.html#T33" target="_self" title="SCMRING3:th.33">Th33</a></i>;<br/><a NAME="E9:99_1_1_1_2"/><b>then </b><i><font color="Green" title="E70">A7</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E10:99_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_2"><i><font color="Green" title="E68">A5</font></i></a></i>;<br/><a NAME="E11:99_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E9:99_1_1_1_2"><i><font color="Green" title="E70">A7</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E13:99_1_1_1_2"/><i><font color="Green" title="E71">A8</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E14:99_1_1_1_2"/><i><font color="Green" title="E72">A9</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><a NAME="E15:99_1_1_1_2"/><i><font color="Green" title="E73">A10</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E8:99_1_1_1_2"><i><font color="Green" title="E69">A6</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E16:99_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_2"><i><font color="Green" title="E68">A5</font></i></a></i>;<br/><a NAME="E17:99_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmring3.html#E15:99_1_1_1_2"><i><font color="Green" title="E73">A10</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E19:99_1_1_1_2"/><i><font color="Green" title="E74">A11</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E20:99_1_1_1_2"/><i><font color="Green" title="E75">A12</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E22:99_1_1_1_2"/><i><font color="Green" title="E76">A13</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c7">I</font>
 <b>and </b><br/><a NAME="E23:99_1_1_1_2"/><i><font color="Green" title="E77">A14</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E13:99_1_1_1_2"><i><font color="Green" title="E71">A8</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">b</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E25:99_1_1_1_2"/><i><font color="Green" title="E78">A15</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_2"><i><font color="Green" title="E65">A2</font></i></a>, <a class="txt" href="scmring3.html#E23:99_1_1_1_2"><i><font color="Green" title="E77">A14</font></i></a>, <a class="ref" href="scmring3.html#T17" target="_self" title="SCMRING3:th.17">Th17</a></i>;<br/><a NAME="E26:99_1_1_1_2"/><i><font color="Green" title="E79">A16</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E22:99_1_1_1_2"><i><font color="Green" title="E76">A13</font></i></a>, <a class="txt" href="scmring3.html#E25:99_1_1_1_2"><i><font color="Green" title="E78">A15</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">J</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E28:99_1_1_1_2"/><i><font color="Green" title="E80">A17</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c10">J</font>
 <b>and </b><br/><a NAME="E29:99_1_1_1_2"/><i><font color="Green" title="E81">A18</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E19:99_1_1_1_2"><i><font color="Green" title="E74">A11</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">d2</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E31:99_1_1_1_2"/><i><font color="Green" title="E82">A19</font></i>: 
<font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c12">d2</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_2"><i><font color="Green" title="E65">A2</font></i></a>, <a class="txt" href="scmring3.html#E29:99_1_1_1_2"><i><font color="Green" title="E81">A18</font></i></a>, <a class="ref" href="scmring3.html#T17" target="_self" title="SCMRING3:th.17">Th17</a></i>;<br/><a NAME="E32:99_1_1_1_2"/><i><font color="Green" title="E83">A20</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E28:99_1_1_1_2"><i><font color="Green" title="E80">A17</font></i></a>, <a class="txt" href="scmring3.html#E31:99_1_1_1_2"><i><font color="Green" title="E82">A19</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E33:99_1_1_1_2"/><i><font color="Green" title="E84">A21</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:99_1_1_1_2"/>
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_1_1_1_2_1"/><i><font color="Green" title="E85">A22</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_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="E1:99_1_1_1_2_1_1"/>
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_2_1"><i><font color="Green" title="E85">A22</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:99_1_1_1_2_1_1_1"/><i><font color="Green" title="E86">A23</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c8">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E14:99_1_1_1_2"><i><font color="Green" title="E72">A9</font></i></a>, <a class="txt" href="scmring3.html#E26:99_1_1_1_2"><i><font color="Green" title="E79">A16</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_2_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_2_1_1_1"><i><font color="Green" title="E86">A23</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:99_1_1_1_2_1_1_2"/><i><font color="Green" title="E86">A24</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c12">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="scmring3.html#E20:99_1_1_1_2"><i><font color="Green" title="E75">A12</font></i></a>, <a class="txt" href="scmring3.html#E32:99_1_1_1_2"><i><font color="Green" title="E83">A20</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_2_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_2_1_1_2"><i><font color="Green" title="E86">A24</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:99_1_1_1_2"/><b>then </b><i><font color="Green" title="E85">A25</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:99_1_1_1_2"><i><font color="Green" title="E67">A4</font></i></a>, <a class="txt" href="scmring3.html#E8:99_1_1_1_2"><i><font color="Green" title="E69">A6</font></i></a>, <a class="txt" href="scmring3.html#E33:99_1_1_1_2"><i><font color="Green" title="E84">A21</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E36:99_1_1_1_2"/>
(  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>hence </b><a NAME="E37:99_1_1_1_2"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_2"><i><font color="Green" title="E65">A2</font></i></a>, <a class="txt" href="scmring3.html#E5:99_1_1_1_2"><i><font color="Green" title="E66">A3</font></i></a>, <a class="txt" href="scmring3.html#E35:99_1_1_1_2"><i><font color="Green" title="E85">A25</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_3"><b>suppose </b></a><a NAME="E1:99_1_1_1_3"/><i><font color="Green" title="E65">A26</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>take </b>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E2:99_1_1_1_3"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T94" title="CARD_3:th.94">CARD_3:94</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:99_1_1_1_3"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:99_1_1_1_3"/><i><font color="Green" title="E66">A27</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:99_1_1_1_3"/><i><font color="Green" title="E67">A28</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:99_1_1_1_3"/><i><font color="Green" title="E68">A29</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/><a NAME="E8:99_1_1_1_3"/><i><font color="Green" title="E69">A30</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_3"><i><font color="Green" title="E65">A26</font></i></a>, <a class="ref" href="scmring3.html#T34" target="_self" title="SCMRING3:th.34">Th34</a></i>;<br/><a NAME="E9:99_1_1_1_3"/><b>then </b><i><font color="Green" title="E70">A31</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E10:99_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_3"><i><font color="Green" title="E68">A29</font></i></a></i>;<br/><a NAME="E11:99_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E9:99_1_1_1_3"><i><font color="Green" title="E70">A31</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E13:99_1_1_1_3"/><i><font color="Green" title="E71">A32</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E14:99_1_1_1_3"/><i><font color="Green" title="E72">A33</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><a NAME="E15:99_1_1_1_3"/><i><font color="Green" title="E73">A34</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E8:99_1_1_1_3"><i><font color="Green" title="E69">A30</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E16:99_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_3"><i><font color="Green" title="E68">A29</font></i></a></i>;<br/><a NAME="E17:99_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmring3.html#E15:99_1_1_1_3"><i><font color="Green" title="E73">A34</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E19:99_1_1_1_3"/><i><font color="Green" title="E74">A35</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E20:99_1_1_1_3"/><i><font color="Green" title="E75">A36</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E22:99_1_1_1_3"/><i><font color="Green" title="E76">A37</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c7">I</font>
 <b>and </b><br/><a NAME="E23:99_1_1_1_3"/><i><font color="Green" title="E77">A38</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E13:99_1_1_1_3"><i><font color="Green" title="E71">A32</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">b</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E25:99_1_1_1_3"/><i><font color="Green" title="E78">A39</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_3"><i><font color="Green" title="E65">A26</font></i></a>, <a class="txt" href="scmring3.html#E23:99_1_1_1_3"><i><font color="Green" title="E77">A38</font></i></a>, <a class="ref" href="scmring3.html#T18" target="_self" title="SCMRING3:th.18">Th18</a></i>;<br/><a NAME="E26:99_1_1_1_3"/><i><font color="Green" title="E79">A40</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E22:99_1_1_1_3"><i><font color="Green" title="E76">A37</font></i></a>, <a class="txt" href="scmring3.html#E25:99_1_1_1_3"><i><font color="Green" title="E78">A39</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">J</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E28:99_1_1_1_3"/><i><font color="Green" title="E80">A41</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c10">J</font>
 <b>and </b><br/><a NAME="E29:99_1_1_1_3"/><i><font color="Green" title="E81">A42</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E19:99_1_1_1_3"><i><font color="Green" title="E74">A35</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">d2</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E31:99_1_1_1_3"/><i><font color="Green" title="E82">A43</font></i>: 
<font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">d2</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_3"><i><font color="Green" title="E65">A26</font></i></a>, <a class="txt" href="scmring3.html#E29:99_1_1_1_3"><i><font color="Green" title="E81">A42</font></i></a>, <a class="ref" href="scmring3.html#T18" target="_self" title="SCMRING3:th.18">Th18</a></i>;<br/><a NAME="E32:99_1_1_1_3"/><i><font color="Green" title="E83">A44</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E28:99_1_1_1_3"><i><font color="Green" title="E80">A41</font></i></a>, <a class="txt" href="scmring3.html#E31:99_1_1_1_3"><i><font color="Green" title="E82">A43</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E33:99_1_1_1_3"/><i><font color="Green" title="E84">A45</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:99_1_1_1_3"/>
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_1_1_1_3_1"/><i><font color="Green" title="E85">A46</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_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="E1:99_1_1_1_3_1_1"/>
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_3_1"><i><font color="Green" title="E85">A46</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:99_1_1_1_3_1_1_1"/><i><font color="Green" title="E86">A47</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c8">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E14:99_1_1_1_3"><i><font color="Green" title="E72">A33</font></i></a>, <a class="txt" href="scmring3.html#E26:99_1_1_1_3"><i><font color="Green" title="E79">A40</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_3_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_3_1_1_1"><i><font color="Green" title="E86">A47</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:99_1_1_1_3_1_1_2"/><i><font color="Green" title="E86">A48</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c12">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="scmring3.html#E20:99_1_1_1_3"><i><font color="Green" title="E75">A36</font></i></a>, <a class="txt" href="scmring3.html#E32:99_1_1_1_3"><i><font color="Green" title="E83">A44</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_3_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_3_1_1_2"><i><font color="Green" title="E86">A48</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:99_1_1_1_3"/><b>then </b><i><font color="Green" title="E85">A49</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:99_1_1_1_3"><i><font color="Green" title="E67">A28</font></i></a>, <a class="txt" href="scmring3.html#E8:99_1_1_1_3"><i><font color="Green" title="E69">A30</font></i></a>, <a class="txt" href="scmring3.html#E33:99_1_1_1_3"><i><font color="Green" title="E84">A45</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E36:99_1_1_1_3"/>
(  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>hence </b><a NAME="E37:99_1_1_1_3"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_3"><i><font color="Green" title="E65">A26</font></i></a>, <a class="txt" href="scmring3.html#E5:99_1_1_1_3"><i><font color="Green" title="E66">A27</font></i></a>, <a class="txt" href="scmring3.html#E35:99_1_1_1_3"><i><font color="Green" title="E85">A49</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_4"><b>suppose </b></a><a NAME="E1:99_1_1_1_4"/><i><font color="Green" title="E65">A50</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>take </b>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E2:99_1_1_1_4"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T94" title="CARD_3:th.94">CARD_3:94</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:99_1_1_1_4"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:99_1_1_1_4"/><i><font color="Green" title="E66">A51</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:99_1_1_1_4"/><i><font color="Green" title="E67">A52</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:99_1_1_1_4"/><i><font color="Green" title="E68">A53</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/><a NAME="E8:99_1_1_1_4"/><i><font color="Green" title="E69">A54</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_4"><i><font color="Green" title="E65">A50</font></i></a>, <a class="ref" href="scmring3.html#T35" target="_self" title="SCMRING3:th.35">Th35</a></i>;<br/><a NAME="E9:99_1_1_1_4"/><b>then </b><i><font color="Green" title="E70">A55</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E10:99_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_4"><i><font color="Green" title="E68">A53</font></i></a></i>;<br/><a NAME="E11:99_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E9:99_1_1_1_4"><i><font color="Green" title="E70">A55</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E13:99_1_1_1_4"/><i><font color="Green" title="E71">A56</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E14:99_1_1_1_4"/><i><font color="Green" title="E72">A57</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><a NAME="E15:99_1_1_1_4"/><i><font color="Green" title="E73">A58</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E8:99_1_1_1_4"><i><font color="Green" title="E69">A54</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E16:99_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_4"><i><font color="Green" title="E68">A53</font></i></a></i>;<br/><a NAME="E17:99_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmring3.html#E15:99_1_1_1_4"><i><font color="Green" title="E73">A58</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E19:99_1_1_1_4"/><i><font color="Green" title="E74">A59</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E20:99_1_1_1_4"/><i><font color="Green" title="E75">A60</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E22:99_1_1_1_4"/><i><font color="Green" title="E76">A61</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c7">I</font>
 <b>and </b><br/><a NAME="E23:99_1_1_1_4"/><i><font color="Green" title="E77">A62</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E13:99_1_1_1_4"><i><font color="Green" title="E71">A56</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">b</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E25:99_1_1_1_4"/><i><font color="Green" title="E78">A63</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_4"><i><font color="Green" title="E65">A50</font></i></a>, <a class="txt" href="scmring3.html#E23:99_1_1_1_4"><i><font color="Green" title="E77">A62</font></i></a>, <a class="ref" href="scmring3.html#T19" target="_self" title="SCMRING3:th.19">Th19</a></i>;<br/><a NAME="E26:99_1_1_1_4"/><i><font color="Green" title="E79">A64</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E22:99_1_1_1_4"><i><font color="Green" title="E76">A61</font></i></a>, <a class="txt" href="scmring3.html#E25:99_1_1_1_4"><i><font color="Green" title="E78">A63</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">J</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E28:99_1_1_1_4"/><i><font color="Green" title="E80">A65</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c10">J</font>
 <b>and </b><br/><a NAME="E29:99_1_1_1_4"/><i><font color="Green" title="E81">A66</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E19:99_1_1_1_4"><i><font color="Green" title="E74">A59</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">d2</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E31:99_1_1_1_4"/><i><font color="Green" title="E82">A67</font></i>: 
<font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">d2</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_4"><i><font color="Green" title="E65">A50</font></i></a>, <a class="txt" href="scmring3.html#E29:99_1_1_1_4"><i><font color="Green" title="E81">A66</font></i></a>, <a class="ref" href="scmring3.html#T19" target="_self" title="SCMRING3:th.19">Th19</a></i>;<br/><a NAME="E32:99_1_1_1_4"/><i><font color="Green" title="E83">A68</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E28:99_1_1_1_4"><i><font color="Green" title="E80">A65</font></i></a>, <a class="txt" href="scmring3.html#E31:99_1_1_1_4"><i><font color="Green" title="E82">A67</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E33:99_1_1_1_4"/><i><font color="Green" title="E84">A69</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:99_1_1_1_4"/>
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_1_1_1_4_1"/><i><font color="Green" title="E85">A70</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_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="E1:99_1_1_1_4_1_1"/>
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_4_1"><i><font color="Green" title="E85">A70</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:99_1_1_1_4_1_1_1"/><i><font color="Green" title="E86">A71</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c8">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E14:99_1_1_1_4"><i><font color="Green" title="E72">A57</font></i></a>, <a class="txt" href="scmring3.html#E26:99_1_1_1_4"><i><font color="Green" title="E79">A64</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_4_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_4_1_1_1"><i><font color="Green" title="E86">A71</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:99_1_1_1_4_1_1_2"/><i><font color="Green" title="E86">A72</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c12">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="scmring3.html#E20:99_1_1_1_4"><i><font color="Green" title="E75">A60</font></i></a>, <a class="txt" href="scmring3.html#E32:99_1_1_1_4"><i><font color="Green" title="E83">A68</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_4_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_4_1_1_2"><i><font color="Green" title="E86">A72</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:99_1_1_1_4"/><b>then </b><i><font color="Green" title="E85">A73</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:99_1_1_1_4"><i><font color="Green" title="E67">A52</font></i></a>, <a class="txt" href="scmring3.html#E8:99_1_1_1_4"><i><font color="Green" title="E69">A54</font></i></a>, <a class="txt" href="scmring3.html#E33:99_1_1_1_4"><i><font color="Green" title="E84">A69</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E36:99_1_1_1_4"/>
(  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>hence </b><a NAME="E37:99_1_1_1_4"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_4"><i><font color="Green" title="E65">A50</font></i></a>, <a class="txt" href="scmring3.html#E5:99_1_1_1_4"><i><font color="Green" title="E66">A51</font></i></a>, <a class="txt" href="scmring3.html#E35:99_1_1_1_4"><i><font color="Green" title="E85">A73</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_5"><b>suppose </b></a><a NAME="E1:99_1_1_1_5"/><i><font color="Green" title="E65">A74</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>take </b>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E2:99_1_1_1_5"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T94" title="CARD_3:th.94">CARD_3:94</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:99_1_1_1_5"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:99_1_1_1_5"/><i><font color="Green" title="E66">A75</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:99_1_1_1_5"/><i><font color="Green" title="E67">A76</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:99_1_1_1_5"/><i><font color="Green" title="E68">A77</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/><a NAME="E8:99_1_1_1_5"/><i><font color="Green" title="E69">A78</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_5"><i><font color="Green" title="E65">A74</font></i></a>, <a class="ref" href="scmring3.html#T36" target="_self" title="SCMRING3:th.36">Th36</a></i>;<br/><a NAME="E9:99_1_1_1_5"/><b>then </b><i><font color="Green" title="E70">A79</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E10:99_1_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_5"><i><font color="Green" title="E68">A77</font></i></a></i>;<br/><a NAME="E11:99_1_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E9:99_1_1_1_5"><i><font color="Green" title="E70">A79</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E13:99_1_1_1_5"/><i><font color="Green" title="E71">A80</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E14:99_1_1_1_5"/><i><font color="Green" title="E72">A81</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><a NAME="E15:99_1_1_1_5"/><i><font color="Green" title="E73">A82</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E8:99_1_1_1_5"><i><font color="Green" title="E69">A78</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E16:99_1_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_5"><i><font color="Green" title="E68">A77</font></i></a></i>;<br/><a NAME="E17:99_1_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmring3.html#E15:99_1_1_1_5"><i><font color="Green" title="E73">A82</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E19:99_1_1_1_5"/><i><font color="Green" title="E74">A83</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E20:99_1_1_1_5"/><i><font color="Green" title="E75">A84</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E22:99_1_1_1_5"/><i><font color="Green" title="E76">A85</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c7">I</font>
 <b>and </b><br/><a NAME="E23:99_1_1_1_5"/><i><font color="Green" title="E77">A86</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E13:99_1_1_1_5"><i><font color="Green" title="E71">A80</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">b</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E25:99_1_1_1_5"/><i><font color="Green" title="E78">A87</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_5"><i><font color="Green" title="E65">A74</font></i></a>, <a class="txt" href="scmring3.html#E23:99_1_1_1_5"><i><font color="Green" title="E77">A86</font></i></a>, <a class="ref" href="scmring3.html#T20" target="_self" title="SCMRING3:th.20">Th20</a></i>;<br/><a NAME="E26:99_1_1_1_5"/><i><font color="Green" title="E79">A88</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E22:99_1_1_1_5"><i><font color="Green" title="E76">A85</font></i></a>, <a class="txt" href="scmring3.html#E25:99_1_1_1_5"><i><font color="Green" title="E78">A87</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">J</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E28:99_1_1_1_5"/><i><font color="Green" title="E80">A89</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c10">J</font>
 <b>and </b><br/><a NAME="E29:99_1_1_1_5"/><i><font color="Green" title="E81">A90</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E19:99_1_1_1_5"><i><font color="Green" title="E74">A83</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">d2</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E31:99_1_1_1_5"/><i><font color="Green" title="E82">A91</font></i>: 
<font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">d2</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_5"><i><font color="Green" title="E65">A74</font></i></a>, <a class="txt" href="scmring3.html#E29:99_1_1_1_5"><i><font color="Green" title="E81">A90</font></i></a>, <a class="ref" href="scmring3.html#T20" target="_self" title="SCMRING3:th.20">Th20</a></i>;<br/><a NAME="E32:99_1_1_1_5"/><i><font color="Green" title="E83">A92</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E28:99_1_1_1_5"><i><font color="Green" title="E80">A89</font></i></a>, <a class="txt" href="scmring3.html#E31:99_1_1_1_5"><i><font color="Green" title="E82">A91</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E33:99_1_1_1_5"/><i><font color="Green" title="E84">A93</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:99_1_1_1_5"/>
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_1_1_1_5_1"/><i><font color="Green" title="E85">A94</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_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="E1:99_1_1_1_5_1_1"/>
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_5_1"><i><font color="Green" title="E85">A94</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:99_1_1_1_5_1_1_1"/><i><font color="Green" title="E86">A95</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c8">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E14:99_1_1_1_5"><i><font color="Green" title="E72">A81</font></i></a>, <a class="txt" href="scmring3.html#E26:99_1_1_1_5"><i><font color="Green" title="E79">A88</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_5_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_5_1_1_1"><i><font color="Green" title="E86">A95</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:99_1_1_1_5_1_1_2"/><i><font color="Green" title="E86">A96</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c12">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="scmring3.html#E20:99_1_1_1_5"><i><font color="Green" title="E75">A84</font></i></a>, <a class="txt" href="scmring3.html#E32:99_1_1_1_5"><i><font color="Green" title="E83">A92</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_5_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_5_1_1_2"><i><font color="Green" title="E86">A96</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:99_1_1_1_5"/><b>then </b><i><font color="Green" title="E85">A97</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:99_1_1_1_5"><i><font color="Green" title="E67">A76</font></i></a>, <a class="txt" href="scmring3.html#E8:99_1_1_1_5"><i><font color="Green" title="E69">A78</font></i></a>, <a class="txt" href="scmring3.html#E33:99_1_1_1_5"><i><font color="Green" title="E84">A93</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E36:99_1_1_1_5"/>
(  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp;  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>hence </b><a NAME="E37:99_1_1_1_5"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_5"><i><font color="Green" title="E65">A74</font></i></a>, <a class="txt" href="scmring3.html#E5:99_1_1_1_5"><i><font color="Green" title="E66">A75</font></i></a>, <a class="txt" href="scmring3.html#E35:99_1_1_1_5"><i><font color="Green" title="E85">A97</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_6"><b>suppose </b></a><a NAME="E1:99_1_1_1_6"/><i><font color="Green" title="E65">A98</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ;<br/><div class="add"><b>take </b>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E2:99_1_1_1_6"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T94" title="CARD_3:th.94">CARD_3:94</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:99_1_1_1_6"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:99_1_1_1_6"/><i><font color="Green" title="E66">A99</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:99_1_1_1_6"/><i><font color="Green" title="E67">A100</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:99_1_1_1_6"/><i><font color="Green" title="E68">A101</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/><a NAME="E8:99_1_1_1_6"/><i><font color="Green" title="E69">A102</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_6"><i><font color="Green" title="E65">A98</font></i></a>, <a class="ref" href="scmring3.html#T37" target="_self" title="SCMRING3:th.37">Th37</a></i>;<br/><a NAME="E9:99_1_1_1_6"/><b>then </b><i><font color="Green" title="E70">A103</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E10:99_1_1_1_6"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_6"><i><font color="Green" title="E68">A101</font></i></a></i>;<br/><a NAME="E11:99_1_1_1_6"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E9:99_1_1_1_6"><i><font color="Green" title="E70">A103</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E13:99_1_1_1_6"/><i><font color="Green" title="E71">A104</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E14:99_1_1_1_6"/><i><font color="Green" title="E72">A105</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><a NAME="E15:99_1_1_1_6"/><i><font color="Green" title="E73">A106</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E8:99_1_1_1_6"><i><font color="Green" title="E69">A102</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E16:99_1_1_1_6"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_6"><i><font color="Green" title="E68">A101</font></i></a></i>;<br/><a NAME="E17:99_1_1_1_6"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmring3.html#E15:99_1_1_1_6"><i><font color="Green" title="E73">A106</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E19:99_1_1_1_6"/><i><font color="Green" title="E74">A107</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E20:99_1_1_1_6"/><i><font color="Green" title="E75">A108</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E22:99_1_1_1_6"/><i><font color="Green" title="E76">A109</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c7">I</font>
 <b>and </b><br/><a NAME="E23:99_1_1_1_6"/><i><font color="Green" title="E77">A110</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E13:99_1_1_1_6"><i><font color="Green" title="E71">A104</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">d1</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c9">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E25:99_1_1_1_6"/><i><font color="Green" title="E78">A111</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c9">r</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_6"><i><font color="Green" title="E65">A98</font></i></a>, <a class="txt" href="scmring3.html#E23:99_1_1_1_6"><i><font color="Green" title="E77">A110</font></i></a>, <a class="ref" href="scmring3.html#T21" target="_self" title="SCMRING3:th.21">Th21</a></i>;<br/><a NAME="E26:99_1_1_1_6"/><i><font color="Green" title="E79">A112</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">r</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E22:99_1_1_1_6"><i><font color="Green" title="E76">A109</font></i></a>, <a class="txt" href="scmring3.html#E25:99_1_1_1_6"><i><font color="Green" title="E78">A111</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">J</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E28:99_1_1_1_6"/><i><font color="Green" title="E80">A113</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c10">J</font>
 <b>and </b><br/><a NAME="E29:99_1_1_1_6"/><i><font color="Green" title="E81">A114</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E19:99_1_1_1_6"><i><font color="Green" title="E74">A107</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">a</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c12">r2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E31:99_1_1_1_6"/><i><font color="Green" title="E82">A115</font></i>: 
<font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c12">r2</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_6"><i><font color="Green" title="E65">A98</font></i></a>, <a class="txt" href="scmring3.html#E29:99_1_1_1_6"><i><font color="Green" title="E81">A114</font></i></a>, <a class="ref" href="scmring3.html#T21" target="_self" title="SCMRING3:th.21">Th21</a></i>;<br/><a NAME="E32:99_1_1_1_6"/><i><font color="Green" title="E83">A116</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E28:99_1_1_1_6"><i><font color="Green" title="E80">A113</font></i></a>, <a class="txt" href="scmring3.html#E31:99_1_1_1_6"><i><font color="Green" title="E82">A115</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E33:99_1_1_1_6"/><i><font color="Green" title="E84">A117</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:99_1_1_1_6"/>
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1_6_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_1_1_1_6_1"/><i><font color="Green" title="E85">A118</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_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="E1:99_1_1_1_6_1_1"/>
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_6_1"><i><font color="Green" title="E85">A118</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_6_1_1_1"><b>suppose </b></a><a NAME="E1:99_1_1_1_6_1_1_1"/><i><font color="Green" title="E86">A119</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c8">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E14:99_1_1_1_6"><i><font color="Green" title="E72">A105</font></i></a>, <a class="txt" href="scmring3.html#E26:99_1_1_1_6"><i><font color="Green" title="E79">A112</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_6_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_6_1_1_1"><i><font color="Green" title="E86">A119</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_6_1_1_2"><b>suppose </b></a><a NAME="E1:99_1_1_1_6_1_1_2"/><i><font color="Green" title="E86">A120</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c12">r2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="scmring3.html#E20:99_1_1_1_6"><i><font color="Green" title="E75">A108</font></i></a>, <a class="txt" href="scmring3.html#E32:99_1_1_1_6"><i><font color="Green" title="E83">A116</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_6_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_6_1_1_2"><i><font color="Green" title="E86">A120</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:99_1_1_1_6"/><b>then </b><i><font color="Green" title="E85">A121</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:99_1_1_1_6"><i><font color="Green" title="E67">A100</font></i></a>, <a class="txt" href="scmring3.html#E8:99_1_1_1_6"><i><font color="Green" title="E69">A102</font></i></a>, <a class="txt" href="scmring3.html#E33:99_1_1_1_6"><i><font color="Green" title="E84">A117</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E36:99_1_1_1_6"/>
(  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c12">r2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 &amp;  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c12">r2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c12">r2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>hence </b><a NAME="E37:99_1_1_1_6"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_6"><i><font color="Green" title="E65">A98</font></i></a>, <a class="txt" href="scmring3.html#E5:99_1_1_1_6"><i><font color="Green" title="E66">A99</font></i></a>, <a class="txt" href="scmring3.html#E35:99_1_1_1_6"><i><font color="Green" title="E85">A121</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_7"><b>suppose </b></a><a NAME="E1:99_1_1_1_7"/><i><font color="Green" title="E65">A122</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><div class="add"><b>take </b>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E2:99_1_1_1_7"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T94" title="CARD_3:th.94">CARD_3:94</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:99_1_1_1_7"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:99_1_1_1_7"/><i><font color="Green" title="E66">A123</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:99_1_1_1_7"/><i><font color="Green" title="E67">A124</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:99_1_1_1_7"/><i><font color="Green" title="E68">A125</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/><a NAME="E8:99_1_1_1_7"/><i><font color="Green" title="E69">A126</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_7"><i><font color="Green" title="E65">A122</font></i></a>, <a class="ref" href="scmring3.html#T38" target="_self" title="SCMRING3:th.38">Th38</a></i>;<br/><a NAME="E9:99_1_1_1_7"/><b>then </b><i><font color="Green" title="E70">A127</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E10:99_1_1_1_7"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_7"><i><font color="Green" title="E68">A125</font></i></a></i>;<br/><a NAME="E11:99_1_1_1_7"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E9:99_1_1_1_7"><i><font color="Green" title="E70">A127</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E13:99_1_1_1_7"/><i><font color="Green" title="E71">A128</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E14:99_1_1_1_7"/><i><font color="Green" title="E72">A129</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E16:99_1_1_1_7"/><i><font color="Green" title="E73">A130</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c6">I</font>
 <b>and </b><br/><a NAME="E17:99_1_1_1_7"/><i><font color="Green" title="E74">A131</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E13:99_1_1_1_7"><i><font color="Green" title="E71">A128</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c7">i1</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E19:99_1_1_1_7"/><i><font color="Green" title="E75">A132</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c7">i1</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_7"><i><font color="Green" title="E65">A122</font></i></a>, <a class="txt" href="scmring3.html#E17:99_1_1_1_7"><i><font color="Green" title="E74">A131</font></i></a>, <a class="ref" href="scmring3.html#T22" target="_self" title="SCMRING3:th.22">Th22</a></i>;<br/><a NAME="E20:99_1_1_1_7"/><i><font color="Green" title="E76">A133</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="ami_1.html#K22" title="AMI_1:func.22">&lt;*</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="ami_1.html#K22" title="AMI_1:func.22">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E21:99_1_1_1_7"/>
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><span class="p1"><a href="ami_1.html#K22" title="AMI_1:func.22">&lt;*</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="ami_1.html#K22" title="AMI_1:func.22">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1_7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_1_1_1_7_1"/>
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:99_1_1_1_7_1"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:99_1_1_1_7_1"/>
<span class="p1"><a href="ami_1.html#K22" title="AMI_1:func.22">&lt;*</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="ami_1.html#K22" title="AMI_1:func.22">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E14:99_1_1_1_7"><i><font color="Green" title="E72">A129</font></i></a>, <a class="txt" href="scmring3.html#E16:99_1_1_1_7"><i><font color="Green" title="E73">A130</font></i></a>, <a class="txt" href="scmring3.html#E19:99_1_1_1_7"><i><font color="Green" title="E75">A132</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/>


</div><b>end;</b></div><a NAME="E22:99_1_1_1_7"/><b>then </b><i><font color="Green" title="E77">A134</font></i>: 
<span class="p1"><a href="ami_1.html#K22" title="AMI_1:func.22">&lt;*</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="ami_1.html#K22" title="AMI_1:func.22">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:99_1_1_1_7"><i><font color="Green" title="E67">A124</font></i></a>, <a class="txt" href="scmring3.html#E8:99_1_1_1_7"><i><font color="Green" title="E69">A126</font></i></a>, <a class="txt" href="scmring3.html#E20:99_1_1_1_7"><i><font color="Green" title="E76">A133</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E23:99_1_1_1_7"/>
(  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c7">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 &amp;  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c7">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="ami_1.html#K22" title="AMI_1:func.22">&lt;*</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="ami_1.html#K22" title="AMI_1:func.22">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>hence </b><a NAME="E24:99_1_1_1_7"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_7"><i><font color="Green" title="E65">A122</font></i></a>, <a class="txt" href="scmring3.html#E5:99_1_1_1_7"><i><font color="Green" title="E66">A123</font></i></a>, <a class="txt" href="scmring3.html#E22:99_1_1_1_7"><i><font color="Green" title="E77">A134</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_8"><b>suppose </b></a><a NAME="E1:99_1_1_1_8"/><i><font color="Green" title="E65">A135</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ;<br/><div class="add"><b>take </b>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_3.html#D14" title="CARD_3:def.14">CARD_3:def 14</a><br/><b>thus </b><a NAME="E2:99_1_1_1_8"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T94" title="CARD_3:th.94">CARD_3:94</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:99_1_1_1_8"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:99_1_1_1_8"/><i><font color="Green" title="E66">A136</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:99_1_1_1_8"/><i><font color="Green" title="E67">A137</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:99_1_1_1_8"/><i><font color="Green" title="E68">A138</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/><a NAME="E8:99_1_1_1_8"/><i><font color="Green" title="E69">A139</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_8"><i><font color="Green" title="E65">A135</font></i></a>, <a class="ref" href="scmring3.html#T39" target="_self" title="SCMRING3:th.39">Th39</a></i>;<br/><a NAME="E9:99_1_1_1_8"/><b>then </b><i><font color="Green" title="E70">A140</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E10:99_1_1_1_8"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_8"><i><font color="Green" title="E68">A138</font></i></a></i>;<br/><a NAME="E11:99_1_1_1_8"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E9:99_1_1_1_8"><i><font color="Green" title="E70">A140</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E13:99_1_1_1_8"/><i><font color="Green" title="E71">A141</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E14:99_1_1_1_8"/><i><font color="Green" title="E72">A142</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><a NAME="E15:99_1_1_1_8"/><i><font color="Green" title="E73">A143</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E8:99_1_1_1_8"><i><font color="Green" title="E69">A139</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E16:99_1_1_1_8"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E7:99_1_1_1_8"><i><font color="Green" title="E68">A138</font></i></a></i>;<br/><a NAME="E17:99_1_1_1_8"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmring3.html#E15:99_1_1_1_8"><i><font color="Green" title="E73">A143</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E19:99_1_1_1_8"/><i><font color="Green" title="E74">A144</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>and </b><br/><a NAME="E20:99_1_1_1_8"/><i><font color="Green" title="E75">A145</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E22:99_1_1_1_8"/><i><font color="Green" title="E76">A146</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c7">I</font>
 <b>and </b><br/><a NAME="E23:99_1_1_1_8"/><i><font color="Green" title="E77">A147</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E13:99_1_1_1_8"><i><font color="Green" title="E71">A141</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">d1</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c9">i1</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E25:99_1_1_1_8"/><i><font color="Green" title="E78">A148</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c9">i1</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_8"><i><font color="Green" title="E65">A135</font></i></a>, <a class="txt" href="scmring3.html#E23:99_1_1_1_8"><i><font color="Green" title="E77">A147</font></i></a>, <a class="ref" href="scmring3.html#T23" target="_self" title="SCMRING3:th.23">Th23</a></i>;<br/><a NAME="E26:99_1_1_1_8"/><i><font color="Green" title="E79">A149</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c8">d1</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E22:99_1_1_1_8"><i><font color="Green" title="E76">A146</font></i></a>, <a class="txt" href="scmring3.html#E25:99_1_1_1_8"><i><font color="Green" title="E78">A148</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">J</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E28:99_1_1_1_8"/><i><font color="Green" title="E80">A150</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c10">J</font>
 <b>and </b><br/><a NAME="E29:99_1_1_1_8"/><i><font color="Green" title="E81">A151</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E19:99_1_1_1_8"><i><font color="Green" title="E74">A144</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">d2</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c12">i2</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E31:99_1_1_1_8"/><i><font color="Green" title="E82">A152</font></i>: 
<font color="Maroon" title="c10">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">d2</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c12">i2</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_8"><i><font color="Green" title="E65">A135</font></i></a>, <a class="txt" href="scmring3.html#E29:99_1_1_1_8"><i><font color="Green" title="E81">A151</font></i></a>, <a class="ref" href="scmring3.html#T23" target="_self" title="SCMRING3:th.23">Th23</a></i>;<br/><a NAME="E32:99_1_1_1_8"/><i><font color="Green" title="E83">A153</font></i>: 
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E28:99_1_1_1_8"><i><font color="Green" title="E80">A150</font></i></a>, <a class="txt" href="scmring3.html#E31:99_1_1_1_8"><i><font color="Green" title="E82">A152</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E33:99_1_1_1_8"/><i><font color="Green" title="E84">A154</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:99_1_1_1_8"/>
for <font color="Olive" title="b1">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_1_1_1_8_1"/><i><font color="Green" title="E85">A155</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_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="E1:99_1_1_1_8_1_1"/>
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_8_1"><i><font color="Green" title="E85">A155</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:99_1_1_1_8_1_1_1"/><i><font color="Green" title="E86">A156</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c9">i1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E14:99_1_1_1_8"><i><font color="Green" title="E72">A142</font></i></a>, <a class="txt" href="scmring3.html#E26:99_1_1_1_8"><i><font color="Green" title="E79">A149</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_8_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_8_1_1_1"><i><font color="Green" title="E86">A156</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:99_1_1_1_8_1_1_2"/><i><font color="Green" title="E86">A157</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c11">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="scmring3.html#E20:99_1_1_1_8"><i><font color="Green" title="E75">A145</font></i></a>, <a class="txt" href="scmring3.html#E32:99_1_1_1_8"><i><font color="Green" title="E83">A153</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:99_1_1_1_8_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_8_1_1_2"><i><font color="Green" title="E86">A157</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:99_1_1_1_8"/><b>then </b><i><font color="Green" title="E85">A158</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:99_1_1_1_8"><i><font color="Green" title="E67">A137</font></i></a>, <a class="txt" href="scmring3.html#E8:99_1_1_1_8"><i><font color="Green" title="E69">A139</font></i></a>, <a class="txt" href="scmring3.html#E33:99_1_1_1_8"><i><font color="Green" title="E84">A154</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E36:99_1_1_1_8"/>
(  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">d2</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c9">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 &amp;  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">d2</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c9">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c11">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><b>hence </b><a NAME="E37:99_1_1_1_8"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="scmring3.html#E1:99_1_1_1_8"><i><font color="Green" title="E65">A135</font></i></a>, <a class="txt" href="scmring3.html#E5:99_1_1_1_8"><i><font color="Green" title="E66">A136</font></i></a>, <a class="txt" href="scmring3.html#E35:99_1_1_1_8"><i><font color="Green" title="E85">A158</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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