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

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/>





<a NAME="E1:66"/><i><font color="Green" title="E65">A1</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T51" title="SCMFSA_2:th.51">SCMFSA_2:51</a></i>;<br/>
<a NAME="E2:66"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self" title="SCMFSA10:th.40">Th40</a></i>;<br/>
<a NAME="E3:66"/><b>then </b><i><font color="Green" title="E66">A2</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:66_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 ;<br/><a NAME="E2:66_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <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#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:66"><i><font color="Green" title="E66">A2</font></i></a>, <a class="ref" href="amistd_2.html#T8" title="AMISTD_2:th.8">AMISTD_2:8</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="E4:66_1"/><i><font color="Green" title="E67">A3</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#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:66_1"/><i><font color="Green" title="E68">A4</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</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="c6">I</font> being   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E7:66_1"/><i><font color="Green" title="E69">A5</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c6">I</font>
 <b>and </b><br/><a NAME="E8:66_1"/><i><font color="Green" title="E70">A6</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E4:66_1"><i><font color="Green" title="E67">A3</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c9">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E10:66_1"/><i><font color="Green" title="E71">A7</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c8">b</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:66"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E8:66_1"><i><font color="Green" title="E70">A6</font></i></a>, <a class="ref" href="scmfsa_2.html#T63" title="SCMFSA_2:th.63">SCMFSA_2:63</a></i>;<br/><a NAME="E11:66_1"/>
<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#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">a</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:66_1"><i><font color="Green" title="E69">A5</font></i></a>, <a class="txt" href="scmfsa10.html#E10:66_1"><i><font color="Green" title="E71">A7</font></i></a>, <a class="ref" href="scmfsa10.html#T27" target="_self" title="SCMFSA10:th.27">Th27</a></i>;<br/><a NAME="E12:66_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:66_1"><i><font color="Green" title="E68">A4</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/><b>hence </b><a NAME="E13:66_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#D5" title="SCMFSA_2:def.5">SCMFSA_2:def 5</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c4">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="E5:66"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c4">x</font> as    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></i>;<br/>
<a NAME="E7:66"/><i><font color="Green" title="E67">A8</font></i>: 
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self" title="SCMFSA10:th.27">Th27</a></i>;<br/>
<a NAME="E8:66"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa10.html#E1:66"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="scmfsa_2.html#T51" title="SCMFSA_2:th.51">SCMFSA_2:51</a></i>;<br/>
<a NAME="E9:66"/><b>then </b><i><font color="Green" title="E68">A9</font></i>: 
<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa10.html#E7:66"><i><font color="Green" title="E67">A8</font></i></a></i>;<br/>
<a NAME="E10:66"/>
<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <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="c5">x</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>
<a NAME="E11:66"/><b>then </b>
<font color="Maroon" title="c5">x</font> <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#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span>,2
 
<b>by </b><i><a class="txt" href="scmfsa10.html#E9:66"><i><font color="Green" title="E68">A9</font></i></a>, <a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/>
<b>hence </b><a NAME="E12:66"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></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="scmfsa10.html#E3:66"><i><font color="Green" title="E66">A2</font></i></a>, <a class="ref" href="amistd_2.html#T8" title="AMISTD_2:th.8">AMISTD_2:8</a></i>;<br/>


</div>
