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

<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> </span><br/>



<a NAME="E1:51"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T45" title="SCMFSA_2:th.45">SCMFSA_2:45</a></span>;<br/>
<a NAME="E2:51"/>
 <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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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="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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T34" target="_self" title="SCMFSA10:th.34">Th34</a>, <a class="ref" href="scmfsa_2.html#T45" title="SCMFSA_2:th.45">SCMFSA_2:45</a></span>;<br/>
<a NAME="E3:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A2</font></span>: 
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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="Red">:: according to </font></span><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> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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 implies <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:51_1"/>
<font color="Maroon" title="c3">x</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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> </span><br/><a NAME="E2:51_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">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#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span>,2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E4:51_1"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
<font color="Maroon" title="c4">f</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> <span class="p1">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:51_1"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
<font color="Maroon" title="c4">f</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="c3">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c5">I</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw"> such that </span><br/><a NAME="E7:51_1"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
<font color="Maroon" title="c4">f</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="c5">I</font>
 <span class="kw">and </span><br/><a NAME="E8:51_1"/><span class="lab"><font color="Green" title="E53">A6</font></span>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:51_1"><span class="lab"><font color="Green" title="E50">A3</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c6">d1</font>, <font color="Maroon" title="c7">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E10:51_1"/><span class="lab"><font color="Green" title="E54">A7</font></span>: 
<font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:51_1"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="scmfsa_2.html#T45" title="SCMFSA_2:th.45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T57" title="SCMFSA_2:th.57">SCMFSA_2:57</a></span>;<br/><font color="Maroon" title="c3">x</font> = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">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
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51_1"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E7:51_1"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="txt" href="#E10:51_1"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="ref" href="scmfsa10.html#T21" target="_self" title="SCMFSA10:th.21">Th21</a></span>
<br/>.= 
<font color="Maroon" title="c7">d2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
;<br/><span class="kw">hence </span><a NAME="E12:51_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#D4" title="SCMFSA_2:def.4">SCMFSA_2:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a>  or <font color="Maroon" title="c3">x</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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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 )</span><br/>

<span class="kw">assume </span><a NAME="E5:51"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">x</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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c3">x</font> as    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a></span>;<br/>
<a NAME="E7:51"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T45" title="SCMFSA_2:th.45">SCMFSA_2:45</a></span>;<br/>
<a NAME="E8:51"/><span class="kw">then </span>
 <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E48">A1</font></span></a></span>;<br/>
<a NAME="E9:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A8</font></span>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span>,2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></span>;<br/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">x</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
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T21" target="_self" title="SCMFSA10:th.21">Th21</a></span>
<br/>.= 
<font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E11:51"/>
<font color="Maroon" title="c3">x</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> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Maroon" title="c1">a</font>,<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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E9:51"><span class="lab"><font color="Green" title="E50">A8</font></span></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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