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

<b>let </b><font color="Maroon" title="c1">i1</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/>



<a NAME="E1:53"/><i><font color="Green" title="E52">A1</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T48" title="SCMFSA_2:th.48">SCMFSA_2:48</a></i>;<br/>
<a NAME="E2:53"/>
 <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#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</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>
 
<b>by </b><i><a class="ref" href="scmfsa10.html#T37" target="_self" title="SCMFSA10:th.37">Th37</a>, <a class="ref" href="scmfsa_2.html#T48" title="SCMFSA_2:th.48">SCMFSA_2:48</a></i>;<br/>
<a NAME="E3:53"/><b>then </b><i><font color="Green" title="E53">A2</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> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span></span>)</span></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/>
<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="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:53_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#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 ;<br/><a NAME="E2:53_1"/><b>then </b>
<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#K20" title="AMI_1:func.20">InsCode</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:53"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="card_3.html#T93" title="CARD_3:th.93">CARD_3:93</a></i>;<br/><b>then consider </b><font color="Maroon" title="c4">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E4:53_1"/><i><font color="Green" title="E54">A3</font></i>: 
<font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:53_1"/><i><font color="Green" title="E55">A4</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</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="c5">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E7:53_1"/><i><font color="Green" title="E56">A5</font></i>: 
<font color="Maroon" title="c4">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="c5">I</font>
 <b>and </b><br/><a NAME="E8:53_1"/><i><font color="Green" title="E57">A6</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E4:53_1"><i><font color="Green" title="E54">A3</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c6">i2</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <font color="Maroon" title="c7">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E10:53_1"/><i><font color="Green" title="E58">A7</font></i>: 
<font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c6">i2</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:53"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E8:53_1"><i><font color="Green" title="E57">A6</font></i></a>, <a class="ref" href="scmfsa_2.html#T60" title="SCMFSA_2:th.60">SCMFSA_2:60</a></i>;<br/><a NAME="E11:53_1"/>
<font color="Maroon" title="c4">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="c6">i2</font>,<font color="Maroon" title="c7">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="scmfsa10.html#E7:53_1"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="scmfsa10.html#E10:53_1"><i><font color="Green" title="E58">A7</font></i></a>, <a class="ref" href="scmfsa10.html#T24" target="_self" title="SCMFSA10:th.24">Th24</a></i>;<br/><a NAME="E12:53_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">i2</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:53_1"><i><font color="Green" title="E55">A4</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="E13:53_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/></div>
<b>end;</b></div>

<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="E5:53"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c3">x</font> as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<a NAME="E7:53"/><i><font color="Green" title="E54">A8</font></i>: 
 <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c4">x</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="c4">x</font>,<font color="Maroon" title="c2">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self" title="SCMFSA10:th.24">Th24</a></i>;<br/>
<a NAME="E8:53"/>
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c4">x</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa10.html#E1:53"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="scmfsa_2.html#T48" title="SCMFSA_2:th.48">SCMFSA_2:48</a></i>;<br/>
<a NAME="E9:53"/><b>then </b><i><font color="Green" title="E55">A9</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="c4">x</font>,<font color="Maroon" title="c2">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></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#K20" title="AMI_1:func.20">InsCode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa10.html#E7:53"><i><font color="Green" title="E54">A8</font></i></a></i>;<br/>
<a NAME="E10:53"/>
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c2">a</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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/>
<a NAME="E11:53"/><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#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span></span>)</span></span>)</span>,1
 
<b>by </b><i><a class="txt" href="scmfsa10.html#E9:53"><i><font color="Green" title="E55">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="E12:53"/>
<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#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span></span>)</span></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="scmfsa10.html#E3:53"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="card_3.html#T93" title="CARD_3:th.93">CARD_3:93</a></i>;<br/>


</div>
